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THE SMOOTHING EFFECT IN SHARP GEVREY SPACE FOR THE SPATIALLY HOMOGENEOUS NON-CUTOFF BOLTZMANN EQUATIONS WITH A HARDPOTENTIAL
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作者 刘吕桥 曾娟 《Acta Mathematica Scientia》 SCIE CSCD 2024年第2期455-473,共19页
In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation e... In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation. We prove that any solution with mild regularity will become smooth in Gevrey class at positive time, with a sharp Gevrey index, depending on the angular singularity. Our proof relies on the elementary L^(2) weighted estimates. 展开更多
关键词 boltzmann equation Gevrey regularity non-cutoff hard potential
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A novel incompressible finite-difference lattice Boltzmann equation for particle-laden flow 被引量:2
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作者 Sheng Chen Zhaohui Liu Baochang Shi Zhu He Chuguang Zheng 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2005年第6期574-581,共8页
In this paper, we propose a novel incompressible finite-difference lattice Boltzmann Equation (FDLBE). Because source terms that reflect the interaction between phases can be accurately described, the new model is s... In this paper, we propose a novel incompressible finite-difference lattice Boltzmann Equation (FDLBE). Because source terms that reflect the interaction between phases can be accurately described, the new model is suitable for simulating two-way coupling incompressible multiphase flow The 2-D particle-laden flow over a backward-facing step is chosen as a test case to validate the present method. Favorable results are obtained and the present scheme is shown to have good prospects in practical applications. 展开更多
关键词 Finite difference lattice boltzmann equation Two-way coupling Multiphase flow INCOMPRESSIBLE
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Investigation on the Dielectric Properties of CO2 and CO2-Based Gases Based on the Boltzmann Equation Analysis 被引量:2
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作者 孙昊 吴翊 +3 位作者 荣命哲 郭安祥 韩桂全 卢彦辉 《Plasma Science and Technology》 SCIE EI CAS CSCD 2016年第3期217-222,共6页
In this paper, the dielectric properties of CO2, CO2/air, CO2/O2, CO2/N2, CO2/CF4, CO2/CH4, CO2/He, C02/H2, CO2/NH3 and CO2/CO were investigated based on the Boltzmann equation analysis, in which the reduced critical ... In this paper, the dielectric properties of CO2, CO2/air, CO2/O2, CO2/N2, CO2/CF4, CO2/CH4, CO2/He, C02/H2, CO2/NH3 and CO2/CO were investigated based on the Boltzmann equation analysis, in which the reduced critical electric field strength (E/N)cr of the gases was derived from the calculated electron energy distribution function (EEDF) by solv- ing the Boltzmann transport equation. In this work, it should be noted that the fundamental data were carefully selected by the published experimental results and calculations to ensure the validity of the calculation. The results indicate that if He, H2, N2 and CH4, in which there axe high ionization coefficients or a lack of attachment reactions, are added into CO2, the dielectric properties will decrease. On the other hand, air, O2, NH3 and CFa (ranked in terms of (E/N)cr value in increasing order) have the potential to improve the dielectric property of CO2 at room temperature. 展开更多
关键词 dielectric property CO2 andysis cross section sets electron energy critical electric field strengthC02 based mixtures boltzmann equation anal-ionization and attachment coefficient reduced
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CAUCHY PROBLEM FOR LINEARIZED NON-CUTOFF BOLTZMANN EQUATION WITH DISTRIBUTION INITIAL DATUM 被引量:1
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作者 李浩光 《Acta Mathematica Scientia》 SCIE CSCD 2015年第2期459-476,共18页
In this article, we study the Cauchy problem for the linearized spatially homogeneous non-cutoff Boltzamnn equation with Maxwellian molecules. By using the spectral decomposition, we solve the Cauchy problem with init... In this article, we study the Cauchy problem for the linearized spatially homogeneous non-cutoff Boltzamnn equation with Maxwellian molecules. By using the spectral decomposition, we solve the Cauchy problem with initial datum in the sense of distribution, which contains the dual space of a Gelfand-Shilov class. We also prove that this solution belongs to the Gelfand-Shilov space for any positive time. 展开更多
关键词 boltzmann equation spectral decomposition Gelfand-Shilov class distribution initial datum
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MACROSCOPIC REGULARITY FOR THE BOLTZMANN EQUATION 被引量:1
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作者 Feimin HUANC Yong WANG 《Acta Mathematica Scientia》 SCIE CSCD 2018年第5期1549-1566,共18页
The regularity of solutions to the Boltzmann equation is a fundamental problem in the kinetic theory. In this paper, the case with angular cut-off is investigated. It is shown that the macroscopic parts of solutions t... The regularity of solutions to the Boltzmann equation is a fundamental problem in the kinetic theory. In this paper, the case with angular cut-off is investigated. It is shown that the macroscopic parts of solutions to the Boltzmann equation, i.e., the density, momentum and total energy are continuous functions of (x, t) in the region R3 × (0, +∞). More precisely, these macroscopic quantities immediately become continuous in any positive time even though they are initially discontinuous and the discontinuities of solutions propagate only in the microscopic level. It should be noted that such kind of phenomenon can not hap- pen for the compressible Navier-Stokes equations in which the initial discontinuities of the density never vanish in any finite time, see [22]. This hints that the Boltzmann equation has better regularity effect in the macroscopic level than compressible Navier-Stokes equations. 展开更多
关键词 boltzmann equation macroscopic regularity compressible Navier-Stokes equations
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BOUNDED SOLUTION OF THE RELATIVISTIC BOLTZMANN EQUATION
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作者 罗兰 喻洪俊 《Acta Mathematica Scientia》 SCIE CSCD 2015年第4期777-786,共10页
In either a periodic box Td or Rd (1 ≤ d ≤ 3), we obtain global bounded solution of the relativistic Boltzmann equation near global relativistic Maxwellian, in terms of natural mass, energy conservation and the en... In either a periodic box Td or Rd (1 ≤ d ≤ 3), we obtain global bounded solution of the relativistic Boltzmann equation near global relativistic Maxwellian, in terms of natural mass, energy conservation and the entropy inequality. 展开更多
关键词 relativistic boltzmann equation relativistic Maxwellian ITERATION global exis-tence
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EXISTENCE OF INFINITE ENERGY SOLUTION TO THE INELASTIC BOLTZMANN EQUATION WITH EXTERNAL FORCE
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作者 魏金波 张显文 《Acta Mathematica Scientia》 SCIE CSCD 2012年第6期2131-2140,共10页
In this paper, the Cauchy problem for the inelastic Boltzmann equation with external force is considered in the case of initial data with infinite energy. More precisely, under the assumptions on the bicharacteristic ... In this paper, the Cauchy problem for the inelastic Boltzmann equation with external force is considered in the case of initial data with infinite energy. More precisely, under the assumptions on the bicharacteristic generated by external force, we prove the global existence of solution for small initial data compared to the local Maxwellian exp(-p|x - v|^2), which has infinite mass and energy. 展开更多
关键词 inelastic boltzmann equation infinite energy external force
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Equivalence Between Forward and Backward Boltzmann Equations in Multi-Component Medium
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作者 张竹林 《Journal of China University of Mining and Technology》 2002年第1期108-110,共3页
The author generalized the propagator function theory introduced first by Sigmund, and gave a explicitly proof of a equivalence between forward and backward Boltzmann equations in a multi component medium by using the... The author generalized the propagator function theory introduced first by Sigmund, and gave a explicitly proof of a equivalence between forward and backward Boltzmann equations in a multi component medium by using the generalized propagator function theory. 展开更多
关键词 suttering boltzmann equation PROPAGATOR
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Asymptotic Solutions of the Kinetic Boltzmann Equation and Multicomponent Non-Equilibrium Gas Dynamics
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作者 S. A. Serov S. S. Serova 《Journal of Applied Mathematics and Physics》 2016年第8期1687-1697,共12页
In the article correct method for the kinetic Boltzmann equation asymptotic solution is formulated, the Hilbert’s and Enskog’s methods are discussed. The equations system of multicomponent non- equilibrium gas dynam... In the article correct method for the kinetic Boltzmann equation asymptotic solution is formulated, the Hilbert’s and Enskog’s methods are discussed. The equations system of multicomponent non- equilibrium gas dynamics is derived, that corresponds to the first order in the approximate (asym- ptotic) method for solution of the system of kinetic Boltzmann equations. 展开更多
关键词 Kinetic boltzmann equation Multicomponent Non-Equilibrium Gas Dynamics
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Gedanken Experiment for Using Boltzmann Equation for Relic Graviton Frequencies, in Pre-Planckian Physics and the Independence of Relic Graviton Density from Either Single Repeating Universe Models or Multiverses
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作者 Andrew Walcott Beckwith 《Journal of High Energy Physics, Gravitation and Cosmology》 2016年第1期83-91,共9页
We look at what may occur if Boltzmann equations, as presented by Murayama in 2007, Les Houches, are applied to graviton density in a pre-Planckian universe setting. Two restrictions are in order. First of all, we are... We look at what may occur if Boltzmann equations, as presented by Murayama in 2007, Les Houches, are applied to graviton density in a pre-Planckian universe setting. Two restrictions are in order. First of all, we are assuming a graviton mass on the order of 10?62 grams, as if the pre-Planckian regime does not change the nature of Graviton mass, in its low end. Secondly, we are also assuming that a comparatively low temperature regime (far below the Planckian temperature) exists. Finally we are leaving unsaid what may happen if Gravitational waves enter the Planck regime of ultra-high temperature. With those three considerations, we proceed to examine a Graviton density value resulting from perturbation from low to higher temperatures. In the end an ultra- hot Pre big bang cosmology will yield essentially no early universe information transfer crossovers to our present cosmological system. This is not affected by the choice if we have a single repeating universe, or a multiverse. A cold pre inflationary state yields a very different situation. Initial frequencies of Gravitons, though, as outlined may be different in the multiverse case, as opposed to the single repeating universe case. We close with comments as to Bicep 2, and how this document has material as to how to avoid the BICEP 2 disaster. And about choosing between either the possibility of massless Scalar-Tensor Gravity as the correct theory of gravitation or conventional GR. 展开更多
关键词 boltzmann equation Stress Energy Tensor Quantum Bounce Infinite Quantum Statistics Heavy Gravity Third Polarization Massless Scalar-Tensor Gravity
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Investigation of Acoustomagnetoelectric Effect in Bandgap Graphene by the Boltzmann Transport Equation
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作者 Raymond Edziah Samuel S. Bentsiefi +6 位作者 Kwadwo Dompreh Anthony Twum Emmanuel Kofi Amewode Patrick Mensah-Amoah Ebenezer T. Tatchie Cynthia Jebuni-Adanu Samuel Y. Mensah 《World Journal of Condensed Matter Physics》 CAS 2024年第1期10-20,共11页
We study the acoustomagnetoelectric (AME) effect in two-dimensional graphene with an energy bandgap using the semiclassical Boltzmann transport equation within the hypersound regime, (where represents the acoustic wav... We study the acoustomagnetoelectric (AME) effect in two-dimensional graphene with an energy bandgap using the semiclassical Boltzmann transport equation within the hypersound regime, (where represents the acoustic wavenumber and is the mean free path of the electron). The Boltzmann transport equation and other relevant equations were solved analytically to obtain an expression for the AME current density, consisting of longitudinal and Hall components. Our numerical results indicate that both components of the AME current densities display oscillatory behaviour. Furthermore, geometric resonances and Weiss oscillations were each defined using the relationship between the current density and Surface Acoustic Wave (SAW) frequency and the inverse of the applied magnetic field, respectively. Our results show that the AME current density of bandgap graphene, which can be controlled to suit a particular electronic device application, is smaller than that of (gapless) graphene and is therefore, more suited for nanophotonic device applications. 展开更多
关键词 boltzmann Transport equation Acoustomagnetoelctric Effect Surface Acoustic Wave Gapless Graphene Weiss Oscillations
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Convergence proof of the DSMC method and the Gas-Kinetic Unified Algorithm for the Boltzmann equation 被引量:12
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作者 LI Zhi Hui FANG Ming +1 位作者 JIANG XinYu WU JunLin 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2013年第2期404-417,共14页
This paper investigates the convergence proof of the Direct Simulation Monte Carlo(DSMC) method and the Gas-Kinetic Unified Algorithm in simulating the Boltzmann equation.It can be shown that the particle velocity dis... This paper investigates the convergence proof of the Direct Simulation Monte Carlo(DSMC) method and the Gas-Kinetic Unified Algorithm in simulating the Boltzmann equation.It can be shown that the particle velocity distribution function obtained by the DSMC method converges to a modified form of the Boltzmann equation,which is the equation of the gas-kinetic unified algorithm to directly solve the molecular velocity distribution function.Their convergence is derived through mathematical treatment.The collision frequency is presented using various molecular models and the local equilibrium distribution function is obtained by Enskog expansion using the converged equation of the DSMC method.These two expressions agree with those used in the unified algorithm.Numerical validation of the converging consistency between these two approaches is illustrated by simulating the pressure driven Poiseuille flow in the slip transition flow regime and the two-dimensional and three-dimensional flows around a circular cylinder and spherical-cone reentry body covering the whole flow regimes from low speed micro-channel flow to high speed non-equilibrium aerothermodynamics. 展开更多
关键词 boltzmann equation DSMC method Gas-Kinetic Unified Algorithm velocity distribution function convergence aerothermodynamics covering flow regimes
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The Gevrey smoothing effect for the spatially inhomogeneous Boltzmann equations without cut-off 被引量:1
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作者 Hua Chen Xin Hu +1 位作者 Wei-Xi Li Jinpeng Zhan 《Science China Mathematics》 SCIE CSCD 2022年第3期443-470,共28页
In this article we study the Gevrey regularization effect for the spatially inhomogeneous Boltzmann equation without angular cut-off.This equation is partially elliptic in the velocity direction and degenerates in the... In this article we study the Gevrey regularization effect for the spatially inhomogeneous Boltzmann equation without angular cut-off.This equation is partially elliptic in the velocity direction and degenerates in the spatial variable.We consider the nonlinear Cauchy problem for the fluctuation around the Maxwellian distribution and prove that any solution with mild regularity will become smooth in the Gevrey class at positive time with the Gevrey index depending on the angular singularity.Our proof relies on the symbolic calculus for the collision operator and the global subelliptic estimate for the Cauchy problem of the linearized Boltzmann operator. 展开更多
关键词 boltzmann equation Gevrey regularity subelliptic estimate non cut-off symbolic calculus
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Convergence Rate to Stationary Solutions for Boltzmann Equation with External Force 被引量:1
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作者 Seiji UKAI Tong YANG Huijiang ZHAO 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2006年第4期363-378,共16页
For the Boltzmann equation with an external force in the form of the gradient of a potential function in space variable, the stability of its stationary solutions as local Maxwellians was studied by S. Ukai et al. (2... For the Boltzmann equation with an external force in the form of the gradient of a potential function in space variable, the stability of its stationary solutions as local Maxwellians was studied by S. Ukai et al. (2005) through the energy method. Based on this stability analysis and some techniques on analyzing the convergence rates to stationary solutions for the compressible Navier-Stokes equations, in this paper, we study the convergence rate to the above stationary solutions for the Boltzmann equation which is a fundamental equation in statistical physics for non-equilibrium rarefied gas. By combining the dissipation from the viscosity and heat conductivity on the fluid components and the dissipation on the non-fluid component through the celebrated H-theorem, a convergence rate of the same order as the one for the compressible Navier-Stokes is obtained by constructing some energy functionals. 展开更多
关键词 Convergence rate boltzmann equation with external force Energy functionals Stationary solutions
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An Exact Solution to the Two-Particle Boltzmann Equation System for Maxwell Gases 被引量:1
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作者 布仁满都拉 赵迎春 《Communications in Theoretical Physics》 SCIE CAS CSCD 2012年第10期565-568,共4页
An exact solution to the two-particle Boltzmann equation system for Maxwell gases is obtained with use of Bobylev approach.The relationship between the exact solution and the self-similar solution of the boltzmann equ... An exact solution to the two-particle Boltzmann equation system for Maxwell gases is obtained with use of Bobylev approach.The relationship between the exact solution and the self-similar solution of the boltzmann equation is also given. 展开更多
关键词 the two-particle boltzmann equation system self-similar solution exact solution
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Thermal Creep Flow for the Boltzmann Equation 被引量:1
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作者 Feimin HUANG 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2015年第5期855-870,共16页
It is known that the Boltzmann equation has close relation to the classical systems in fluid dynamics. However, it provides more information on the microscopic level so that some phenomena, like the thermal creep flow... It is known that the Boltzmann equation has close relation to the classical systems in fluid dynamics. However, it provides more information on the microscopic level so that some phenomena, like the thermal creep flow, can not be modeled by the classical systems of fluid dynamics, such as the Euler equations. The author gives an example to show this phenomenon rigorously in a special setting. This paper is completely based on the author's recent work, jointly with Wang and Yang. 展开更多
关键词 Thermal creep flow Non-classical fluid system boltzmann equation
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STABILITY OF DISSIPATIVE BOLTZMANN EQUATION FOR ONE-DIMENSIONAL GRANULAR GASES 被引量:2
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作者 Shoubo Jin, Panfeng Chen (School of Math. and Statistics, Suzhou University, Suzhou 234000, Anhui) 《Annals of Differential Equations》 2011年第2期145-149,共5页
In this paper, the stability of the dissipative Boltzmann equation is investigated under the influence of an external source of energy for the spatially homogeneous case. Using probability distance, we give an estimat... In this paper, the stability of the dissipative Boltzmann equation is investigated under the influence of an external source of energy for the spatially homogeneous case. Using probability distance, we give an estimate to show the uniform stability of the solution. 展开更多
关键词 dissipative boltzmann equation STABILITY Fourier transform
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Exponential Runge-Kutta Methods for the Multispecies Boltzmann Equation 被引量:1
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作者 Qin Li Xu Yang 《Communications in Computational Physics》 SCIE 2014年第4期996-1011,共16页
This paper generalizes the exponential Runge-Kutta asymptotic preserving(AP)method developed in[G.Dimarco and L.Pareschi,SIAM Numer.Anal.,49(2011),pp.2057–2077]to compute the multi-species Boltzmann equation.Compared... This paper generalizes the exponential Runge-Kutta asymptotic preserving(AP)method developed in[G.Dimarco and L.Pareschi,SIAM Numer.Anal.,49(2011),pp.2057–2077]to compute the multi-species Boltzmann equation.Compared to the single species Boltzmann equation that the method was originally applied on,this set of equation presents a new difficulty that comes from the lack of local conservation laws due to the interaction between different species.Hence extra stiff nonlinear source terms need to be treated properly to maintain the accuracy and the AP property.The method we propose does not contain any nonlinear nonlocal implicit solver,and can capture the hydrodynamic limit with time step and mesh size independent of the Knudsen number.We prove the positivity and strong AP properties of the scheme,which are verified by two numerical examples. 展开更多
关键词 Multispecies boltzmann equation exponential Runge-Kutta method hydrodynamic limit asymptotic preserving property positivity preserving
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Boltzmann Equations with Quantum Effects (2): Entropy Identity, Existence and Uniqueness of Spatial Decay Solutions
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作者 张英魁 卢旭光 《Tsinghua Science and Technology》 SCIE EI CAS 2002年第3期219-222,共4页
A previous study is continued by investigating the Boltzmann equation for particles with quantum effects (BQE). First, the corresponding entropy identity is proved, then if the initial data f(x,v,0) satisfies 0... A previous study is continued by investigating the Boltzmann equation for particles with quantum effects (BQE). First, the corresponding entropy identity is proved, then if the initial data f(x,v,0) satisfies 0≤f(x,v,0)≤CΦ(x,v,0) for a constant 0<C<∞ and function Φ(x,v,t), we prove the existence and uniqueness of spatial decay solutions of the BQE within a given function space B(Φ) using fixed point theory. Moreover, if there is a continuous function F(x,v) which belongs to a function set, then there exists a mild solution f(x,v,t) of the BQE such that f ∞(x,v)= limt→∞f(x+vt,v,t)=F(x,v). 展开更多
关键词 boltzmann equation quantum effects EXISTENCE UNIQUENESS entropy identity spatial decay
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Globally hyperbolic moment model of arbitrary order for the three-dimensional special relativistic Boltzmann equation with the Anderson-Witting collision
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作者 Yangyu Kuang Huazhong Tang 《Science China Mathematics》 SCIE CSCD 2022年第5期1029-1064,共36页
This paper continues to derive the globally hyperbolic moment model of arbitrary order for the three-dimensional special relativistic Boltzmann equation with the Anderson-Witting collision.The method is the model redu... This paper continues to derive the globally hyperbolic moment model of arbitrary order for the three-dimensional special relativistic Boltzmann equation with the Anderson-Witting collision.The method is the model reduction by the operator projection.Finding an orthogonal basis of the weighted polynomial space is crucial and built on infinite families of the complicate relativistic Grad type orthogonal polynomials depending on a parameter and the real spherical harmonics instead of the irreducible tensors.We study the properties of those functions carefully,including their recurrence relations,their derivatives with respect to the independent variable and the parameter,and the zeros of the orthogonal polynomials.Our moment model is proved to be globally hyperbolic and linearly stable.Moreover,the Lorentz covariance,the quasi-one-dimensional case,and the non-relativistic and ultra-relativistic limits are also studied. 展开更多
关键词 moment method HYPERBOLICITY special relativistic boltzmann equation model reduction operator projection
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