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TIME DECAY RATE OF SOLUTIONS TO THE HYPERBOLIC MHD EQUATIONS IN R3 被引量:1
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作者 李蓓 朱红锦 赵才地 《Acta Mathematica Scientia》 SCIE CSCD 2016年第5期1369-1382,共14页
In this paper, we first show the global existence, uniqueness and regularity of weak solutions for the hyperbolic magnetohydrodynamics(MHD) equations in R^3. Then we establish that the solutions with initial data belo... In this paper, we first show the global existence, uniqueness and regularity of weak solutions for the hyperbolic magnetohydrodynamics(MHD) equations in R^3. Then we establish that the solutions with initial data belonging to H^m(R^3) ∩ L^1(R^3) have the following time decay rate:║▽~mu(x, t) ║~2+║ ▽~mb(x, t)║~ 2+ ║▽^(m+1)u(x, t)║~ 2+ ║▽^(m+1)b(x, t) ║~2≤ c(1 + t)^(-3/2-m)for large t, where m = 0, 1. 展开更多
关键词 hyperbolic MHD equations weak solution time decay rate
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Time Decay Rate of Solutions Toward the Viscous Shock Waves under Periodic Perturbations for the Scalar Conservation Law with Nonlinear Viscosity
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作者 Ye-chi LIU 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2023年第1期28-48,共21页
In this paper,it is proved that the weak solution to the Cauchy problem for the scalar viscous conservation law,with nonlinear viscosity,different far field states and periodic perturbations,not only exists globally i... In this paper,it is proved that the weak solution to the Cauchy problem for the scalar viscous conservation law,with nonlinear viscosity,different far field states and periodic perturbations,not only exists globally in time,but also converges towards the viscous shock wave of the corresponding Riemann problem as time goes to infinity.Furthermore,the decay rate is shown.The proof is given by a technical energy method. 展开更多
关键词 viscous conservation law asymptotic behavior time decay rate viscous shock wave periodic perturbation
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TIME PERIODIC SOLUTIONS OF NON-ISENTROPIC COMPRESSIBLE MAGNETOHYDRODYNAMIC SYSTEM
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作者 许秋菊 蔡虹 谭忠 《Acta Mathematica Scientia》 SCIE CSCD 2015年第1期216-234,共19页
In this paper, we study the non-isentropic compressible magnetohydrodynamic system with a time periodic external force in R^n. Under the condition that the optimal time decay rates are obtained by spectral analysis, w... In this paper, we study the non-isentropic compressible magnetohydrodynamic system with a time periodic external force in R^n. Under the condition that the optimal time decay rates are obtained by spectral analysis, we show that the existence, uniqueness and time-asymptotic stability of time periodic solutions when the space dimension n 〉 5. Our proof is based on a combination of the energy method and the contraction mapping theorem. 展开更多
关键词 non-isentropic compressible magnetohydrodynamic system time periodic solution optimal time decay rates energy estimates
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THE GLOBAL EXISTENCE AND A DECAY ESTIMATE OF SOLUTIONS TO THE PHAN-THEIN-TANNER MODEL
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作者 Ruiying WEI Yin LI Zheng-an YAO 《Acta Mathematica Scientia》 SCIE CSCD 2022年第3期1058-1080,共23页
In this paper,we study the global existence and decay rates of strong solutions to the three dimensional compressible Phan-Thein-Tanner model.By a refined energy method,we prove the global existence under the assumpti... In this paper,we study the global existence and decay rates of strong solutions to the three dimensional compressible Phan-Thein-Tanner model.By a refined energy method,we prove the global existence under the assumption that the H^(3) norm of the initial data is small,but that the higher order derivatives can be large.If the initial data belong to homogeneous Sobolev spaces or homogeneous Besov spaces,we obtain the time decay rates of the solution and its higher order spatial derivatives.Moreover,we also obtain the usual L^(p)-L^(2)(1≤p≤2)type of the decay rate without requiring that the Lpnorm of initial data is small. 展开更多
关键词 Phan-Thein-Tanner model global existence time decay rates
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Global Existence and Decay of Solution to Parabolic-Parabolic Keller-Segel Model in R^(d)
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作者 ZHONG Wenbin LIU Xiaofeng 《Journal of Donghua University(English Edition)》 CAS 2022年第1期85-94,共10页
We consider the global existence and decay of integral solutions to the parabolic-parabolic Keller-Segel system in d-dimension.On the one hand,by Banach fixed point theorem and some properties of heat kernel,we prove ... We consider the global existence and decay of integral solutions to the parabolic-parabolic Keller-Segel system in d-dimension.On the one hand,by Banach fixed point theorem and some properties of heat kernel,we prove the local existence and the global existence of integral solutions for the different initial data under some conditions that involve the size of the initial data.On the other hand,in the case of global solutions,we obtain their optimal time decay by Gronwall’s lemma. 展开更多
关键词 Keller-Segel system global existence integral solution local existence optimal time decay rate
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Spectrum structure and decay rate estimates on the Landau equation with Coulomb potential
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作者 Tong Yang Hongjun Yu 《Science China Mathematics》 SCIE CSCD 2023年第1期37-78,共42页
In this paper we first deduce the estimates on the linearized Landau operator with Coulomb potential and then analyze its spectrum structure by using semigroup theory and linear operator perturbation theory.Based on t... In this paper we first deduce the estimates on the linearized Landau operator with Coulomb potential and then analyze its spectrum structure by using semigroup theory and linear operator perturbation theory.Based on these estimates,we give the precise time decay rate estimates on the semigroup generated by the linearized Landau operator so that the optimal time decay rates of the nonlinear Landau equation follow.In addition,we present a similar result for the non-angular cutoff Boltzmann equation with soft potentials. 展开更多
关键词 spectrum structure time decay rate Landau equation Boltzmann equation
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Optimal time-decay rates of the Boltzmann equation
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作者 ZHONG MingYing 《Science China Mathematics》 SCIE 2014年第4期807-822,共16页
We consider the optimal time-convergence rates of the global solution to the Cauchy problem for the Boltzmann equation in R3.We show that the global solution tends to the global Maxwellian at the optimal time-decay ra... We consider the optimal time-convergence rates of the global solution to the Cauchy problem for the Boltzmann equation in R3.We show that the global solution tends to the global Maxwellian at the optimal time-decay rate(1+t)-3/4,where the macroscopic density,momentum and energy decay at the optimal rate(1+t)-3/4 and the microscopic part decays at the optimal rate(1+t)-5/4.We also show that the solution tends to the Maxwellian at the optimal time-decay rate(1+t).5/4 in the case of the macroscopic part of the initial data is zero,where the macroscopic density,momentum and energy decay at the optimal rate(1+t)-5/4 and the microscopic part decays at the optimal rate(1+t)-7/4.These convergence rates are shown to be optimal for the Boltzmann equation. 展开更多
关键词 Boltzmann equation optimal time decay rate
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COMPRESSIBLE NAVIER-STOKES-POISSON EQUATIONS 被引量:3
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作者 肖玲 李海梁 《Acta Mathematica Scientia》 SCIE CSCD 2010年第6期1937-1948,共12页
This is a survey paper on the study of compressible Navier-Stokes-Poisson equations. The emphasis is on the long time behavior of global solutions to multi-dimensional compressible Navier-Stokes-Poisson equations, and... This is a survey paper on the study of compressible Navier-Stokes-Poisson equations. The emphasis is on the long time behavior of global solutions to multi-dimensional compressible Navier-Stokes-Poisson equations, and the optimal decay rates for both unipolar and bipolar compressible Navier-Stokes-Poisson equations are discussed. 展开更多
关键词 Navier-Stokes-Poisson system optimal time decay rates
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COMPRESSIBLE NON-ISENTROPIC BIPOLAR NAVIER-STOKES-POISSON SYSTEM IN R^3 被引量:1
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作者 肖玲 李海梁 +1 位作者 杨彤 邹晨 《Acta Mathematica Scientia》 SCIE CSCD 2011年第6期2169-2194,共26页
The compressible non-isentropic bipolar Navier-Stokes-Poisson (BNSP) sys- tem is investigated in R3 in the present paper, and the optimal time decay rates of global strong solution are shown. For initial data being ... The compressible non-isentropic bipolar Navier-Stokes-Poisson (BNSP) sys- tem is investigated in R3 in the present paper, and the optimal time decay rates of global strong solution are shown. For initial data being a perturbation of equilibrium state in Hl(R3) (R3) for 1 〉 4 and s E (0, 1], it is shown that the density and temperature for each charged particle (like electron or ion) decay at the same optimal rate (1 + t)-3/4, but the momentum for each particle decays at the optimal rate (1 + t)-1/4-3/2 which is slower than the rate (1 + t)-3/4-3/2 for the compressible Navier-Stokes (NS) equations [19] for same initial data. However, the total momentum tends to the constant state at the rate (1 +t)-3/4 as well, due to the interplay interaction of charge particles which counteracts the influence of electric field. 展开更多
关键词 Non-isentropic bipolar Navier-Stokes Poisson system optimal time decay rate
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THE VLASOV-MAXWELL-FOKKER-PLANCK SYSTEM WITH RELATIVISTIC TRANSPORT IN THE WHOLE SPACE
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作者 杨东成 《Acta Mathematica Scientia》 SCIE CSCD 2017年第5期1237-1261,共25页
In this paper, we consider the Vlasov-Maxwell-Fokker-Planck system with relativistic transport in the whole space. The global solutions to this system near the relativistic Maxwellian are constructed and the optimal t... In this paper, we consider the Vlasov-Maxwell-Fokker-Planck system with relativistic transport in the whole space. The global solutions to this system near the relativistic Maxwellian are constructed and the optimal time decay rate of global solutions are also obtained by an approach by combining the compensating function and energy method. 展开更多
关键词 relativistic Vlasov-Maxwell-Fokker-Planck system compensating function global solutions optimal time decay rate
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A Note on Time-Decay Estimates for the Compressible Navier–Stokes Equations
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作者 Jiang XU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2018年第4期662-680,共19页
In the recent work, we have developed a decay framework in general Lp critical spaces and established optimal time-decay estimates for barotropic compressible Navier-Stokes equations. Those decay rates of Lq-Lr type o... In the recent work, we have developed a decay framework in general Lp critical spaces and established optimal time-decay estimates for barotropic compressible Navier-Stokes equations. Those decay rates of Lq-Lr type of the solution and its derivatives are available in the critical regularity framework, which were exactly firstly observed by Matsumura & Nishida, and subsequently generalized by Ponce for solutions with high Sobolev regularity. We would like to mention that our approach is likely to be effective for other hyperbolic/parabolic systems that are encountered in fluid mechanics or mathematical physics. In this paper, a new observation is involved in the high frequency, which enables us to improve decay exponents for the high frequencies of solutions. 展开更多
关键词 time decay rates Navier Stokes equations Lp critical spaces
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Asymptotical Behavior of Bipolar Non-Isentropic Compressible Navier-Stokes-Poisson System
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作者 Chen ZOU 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2016年第4期813-832,共20页
Abstract The bipolar non-isentropic compressible Navier-Stokes-Poisson (BNSP) system is investigated in R3 in the present paper, and the optimal L2 time decay rate for the global classical solution is established. I... Abstract The bipolar non-isentropic compressible Navier-Stokes-Poisson (BNSP) system is investigated in R3 in the present paper, and the optimal L2 time decay rate for the global classical solution is established. It is shown that the total densities, total momenta and total temperatures of two carriers converge to the equilibrium states at the rate (1 + t)-3/4+εin L2-norm for any small and fix ε 〉 0. But, both the difference of densities and the difference of temperatures of two carriers decay at the optimal rate (1 + t)- 3/4, and the difference of momenta decays at the optimal rate (1 +t)- 1/4. This phenomenon on the charge transport shows the essential difference between the non-isentropic unipolar NSP and the bipolar NSP system. 展开更多
关键词 non-isentropic bipolar Navier-Stokes-Poisson system optimal time decay rate
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