INTERFACE BEHAVIOR AND DECAY RATES OF COMPRESSIBLE NAVIER-STOKES SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND A VACUUM

In this paper,we study the one-dimensional motion of viscous gas near a vacuum,with the gas connecting to a vacuum state with a jump in density.The interface behavior,the pointwise decay rates of the density function and the expanding rates of the interface are obtained with the viscosity coefficientμ(ρ)=ρ^(α)for any 0<α<1;this includes the timeweighted boundedness from below and above.The smoothness of the solution is discussed.Moreover,we construct a class of self-similar classical solutions which exhibit some interesting properties,such as optimal estimates.The present paper extends the results in[Luo T,Xin Z P,Yang T.SIAM J Math Anal,2000,31(6):1175-1191]to the jump boundary conditions case with density-dependent viscosity.

GLOBAL WELL-POSEDNESS AND OPTIMAL TIME DECAY RATES FOR THE GENERALIZED PHAN-THIEN-TANNER MODEL IN R^(3)

In this paper, we consider the initial value problem for the incompressible generalized Phan-Thien-Tanner(GPTT) model. This model pertains to the dynamic properties of polymeric fluids. Under appropriate assumptions on smooth function f, we find a particular solution to the GPTT model. In dimension three, we establish the global existence and the optimal time decay rates of strong solutions provided that the initial data is close to the particular solution. The results which are presented here are generalizations of the network viscoelastic models.

Decay rates and time lags of heat conduction in building construction under field conditions

The field measurements of decay rates and time lags of heat conduction in a building construction taken in Nanjing during the summer of 2001 are presented.The decay rates and time lags are calculated according to the frequency responses of the heat absorbed by the room＇s internal surfaces,inside surface temperature,indoor air temperature and outdoor synthetic temperature.The measured results match very well with the theoretical results of the zeroth and the first order values of the decay rates and time lags of heat conduction in the building construction,but the difference between the measured values and the theoretical values for the second order is too great to be accepted.It is therefore difficult to accurately test the second order value.However,it is still advisable to complete the analysis using the zeroth-and the first-orders values of the decay rates and time lags of heat conduction in building construction under field conditions,because in these cases the decay rates of heat conduction reach twenty which meets the requirements of engineering plans.

DECAY RATES OF PLANAR VISCOUS RAREFACTION WAVE FOR MULTI-DIMENSIONAL SCALAR CONSERVATION LAW WITH DEGENERATE VISCOSITY ON HALF SPACE

We investigate the decay rates of the planar viscous rarefaction wave of the initial-boundary value problem to scalar conservation law with degenerate viscosity in several dimensions on the half-line space, where the corresponding one-dimensional problem admits the rarefaction wave as an asymptotic state. The analysis is based on the standard L2-energy method and L1-estimate.

Influence of Thermal Radiation on Hot Cluster Decay Rates and Abundances

The influence of radiative cooling on the unimolecular decay rates of free, hot clusters and molecules with unspecified excitation energies is quantified. Two different regimes, dedined by the magnitude of the energy of the photons emitted, are identified and the boundary between them is given. The boundary is determined in terms of the photon emission rate constants and thermal properties of the particles. Also the abundance spectra are calculated for the continuous cooling case, corresponding to small photon energies. The two regimes correspond to continuous cooling and single photon quenching of the unimolecular decay. The radiative effect can be parametrized by a redefinition of the time each individual cluster has available to undergo evaporation, expressed by an effective radiative time constant.

THE TIME DECAY RATES OF THE CLASSICAL SOLUTION TO THE POISSON-NERNST-PLANCK-FOURIER EQUATIONS IN R^(3)

In this work,the Poisson-Nernst-Planck-Fourier system in three dimensions is considered.For when the initial data regards a small perturbation around the constant equilibrium state in a H^(3)∩■^(-s)(0≤s≤1/2)norm,we obtain the time convergence rate of the global solution by a regularity interpolation trick and an energy method.

Decay rates of higher-order norms of solutions to the Navier-Stokes-Landau-Lifshitz system

In this paper, we investigate a system of the incompressible Navier-Stokes equations coupled with Landau-Lifshitz equations in three spatial dimensions. Under the assumption of small initial data, we establish the global solutions with the help of an energy method. Furthermore, we obtain the time decay rates of the higher-order spatial derivatives of the solutions by applying a Fourier splitting method introduced by Schonbek(SCHONBEK, M. E. L2decay for weak solutions of the Navier-Stokes equations. Archive for Rational Mechanics and Analysis, 88, 209–222(1985)) under an additional assumption that the initial perturbation is bounded in L1(R3).

A solution of the complex Ginzburg-Landau equation with a continuum of decay rates

We prove the existence of a uniform initial datum whose solution decays, in var- ious Lp spaces, at different rates along different time sequences going to infinity, for complex Ginzburg-Landau equation on RN, of various parameters θ and γ.

Re-analysis of temperature dependent neutron capture rates and stellarβ-decay rates of^(95-98)Mo

The neutron capture rates and temperature dependent stellar beta decay rates of Mo isotopes are investigated within the framework of the statistical code TALYS v1.96 and the proton neutron quasi particle random phase approximation(pn-QRPA)model.The Maxwellian average cross-section(MACS)and neutron capture rates for the^(95-98)Mo(n,γ)^(96-99)Mo radiative capture process are analyzed within the framework of the statistical code TALYS v1.96 based on the phenomenological nuclear level density model and gamma strength functions.The present model-based computations for the MACS are comparable to the existing measured data.The sensitivity of stellar weak interaction rates to various densities and temperatures is investigated within the framework of the pn-QRPA model.Particular attention is paid to the impact of thermally filled excited states in the decaying nuclei(^(95-98)Mo)on electron emission and positron capture rates.Furthermore,we compare the neutron capture rates and stellar beta decay rates.It is found that neutron capture rates are higher than stellar beta decay rates at both lower and higher temperatures.

The sharp time-decay rates for one-dimensional compressible isentropic Navier-Stokes and magnetohydrodynamic flows

In this paper, we investigate the large-time behavior of strong solutions to the Cauchy problem for one-dimensional compressible isentropic magnetohydrodynamic equations near a stable equilibrium. The difference between the one-dimensional and multi-dimensional cases is a feature for compressible flows and also brings new difficulties. In contrast to the multi-dimensional case, the decay rates of nonlinear terms may not be faster than linear terms in dimension one. To handle this, we shall present a new energy estimate in terms of a combination of the solutions with small initial data. We aim to establish the sharp upper and lower bounds on the L^(2)-decay rates of the solutions and all their spatial derivatives when the initial perturbation is small in L^(1)(R) ∩ H^(2)(R). It is worth noticing that there is no decay loss for the highest-order spatial derivatives of the solutions so that the large-time behavior for the hyperbolic-parabolic system is exactly sharp. As a byproduct, the above result is also valid for compressible Navier-Stokes equations. Our approach is based on various interpolation inequalities, energy estimates, spectral analysis, and Fourier time-splitting and high-low frequency decomposition methods.

Global existence and time decay rates for the 3D bipolar compressible Navier-Stokes-Poisson system with unequal viscosities

We consider the Cauchy problem for the three-dimensional bipolar compressible Navier-Stokes-Poisson system with unequal viscosities.Under the assumption that the H_(3) norm of the initial data is small but its higher order derivatives can be arbitrarily large,the global existence and uniqueness of smooth solutions are obtained by an ingenious energy method.Moreover,if additionally,the H^(−s)(1/2≤s<3/2)or B^(−s)_(2,∞)(1/2<s≤3/2)norm of the initial data is small,the optimal decay rates of solutions are also established by a regularity interpolation trick and delicate energy methods.

Environmental effects on nuclear decay rates

The possible change of nuclear decay rates in different environments has long been an interesting topic due to its importance not only in nuclear physics but also in astrophysics, geological dating, condensed matter physics, etc. The progress in the investigation of variations in nuclear decay rates are reviewed.

Optimal time-decay rates of the Boltzmann equation

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.

THE OPTIMAL LARGE TIME BEHAVIOR OF3D QUASILINEAR HYPERBOLIC EQUATIONS WITH NONLINEAR DAMPING

We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third order spatial derivatives of the solution,which are the same as those of the heat equation,and in particular,are faster than ones of previous related works.Second,for well-chosen initial data,we also show that the lower optimal L^(2) convergence rate of the k(∈[0,3])-order spatial derivatives of the solution is(1+t)^(-(2+2k)/4).Therefore,our decay rates are optimal in this sense.The proofs are based on the Fourier splitting method,low-frequency and high-frequency decomposition,and delicate energy estimates.

DECAY ESTIMATES OF PLANAR STATIONARY WAVES FOR DAMED WAVE EQUATIONS WITH NONLINEAR CONVECTION IN MULTI-DIMENSIONAL HALF SPACE

This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the multi-dimensional half space R n ＋ ： u tt u ＋ u t ＋ divf （u） = 0, t 〉 0, x = （x 1 , x ′ ） ∈ R n ＋ ：= R ＋ × R n 1 , u（0, x） = u 0 （x） → u ＋ , as x 1 → ＋ ∞ , u t （0, x） = u 1 （x）, u（t, 0, x ′ ） = u b , x ′ = （x 2 , x 3 , ··· , x n ） ∈ R n 1 . （I） For the non-degenerate case f ′ 1 （u ＋ ） 〈 0, it was shown in [10] that the above initialboundary value problem （I） admits a unique global solution u（t, x） which converges to the corresponding planar stationary wave φ（x 1 ） uniformly in x 1 ∈ R ＋ as time tends to infinity provided that the initial perturbation and/or the strength of the stationary wave are sufficiently small. And in [10] Ueda, Nakamura, and Kawashima proved the algebraic decay estimates of the tangential derivatives of the solution u（t, x） for t → ＋ ∞ by using the space-time weighted energy method initiated by Kawashima and Matsumura [5] and improved by Nishihkawa [7]. Moreover, by using the same weighted energy method, an additional algebraic convergence rate in the normal direction was obtained by assuming that the initial perturbation decays algebraically. We note, however, that the analysis in [10] relies heavily on the assumption that f ′ （u） 〈 0. The main purpose of this paper isdevoted to discussing the case of f ′ 1 （u b ） ≥ 0 and we show that similar results still hold for such a case. Our analysis is based on some delicate energy estimates.

THE GLOBAL EXISTENCE AND ANALYTICITY OF A MILD SOLUTION TO THE 3D REGULARIZED MHD EQUATIONS

In this paper,we study the three-dimensional regularized MHD equations with fractional Laplacians in the dissipative and diffusive terms.We establish the global existence of mild solutions to this system with small initial data.In addition,we also obtain the Gevrey class regularity and the temporal decay rate of the solution.

THE DECAY ESTIMATES FOR MAGNETOHYDRODYNAMIC EQUATIONS WITH COULOMB FORCE

In this article we consider the compressible viscous magnetohydrodynamic equations with Coulomb force.By spectral analysis and energy methods,we obtain the optimal time decay estimate of the solution.We show that the global classical solution converges to its equilibrium state at the same decay rate as the solution of the linearized equations.

THE GLOBAL EXISTENCE AND A DECAY ESTIMATE OF SOLUTIONS TO THE PHAN-THEIN-TANNER MODEL

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.

A Remark on the Time Decay of Non-Newtonian Flows in R3

In the study of long time asymptotic behaviors of the solutions to a class system of the incompressible non-Newtonian fluid flows in R3, it is proved that the weak solutions decay in L2 norm at （1 ＋ t）- 3/4 and the error of difference between non-Newtonian fluid and linear equation is also investigated. The findings are mainly based on the classic Fourier splitting methods.

The decay kinetics of residual chlorine in cooling seawater simulation experiments

To find out the decay character of residual chlorine （RC） in the sea water, the concentration of RC was analyzed by N, N-diethyl-p-phenylenediamine （DPD） method under different simulation experimental conditions, in which salinity, temperature, and Chemical Oxygen Demand （COD） were selected. The water used in the experiment was the mixture of aging ocean water, coastal water and extracting solution of coastal sediment at appropriate level. Results are shown as follows： （1） Piecewise function can well reflect the decay dynamics of RC in the cooling seawater. Concretely, the decay dynamics of first 1 min is too rapid to ascertain using a specific kinetic function, and that of the time from 1 to 30 min is fit for the first-order kinetic model. （2） The results could be the foundation of the chemical behavior of RC in seawater, and be used as not only the guidance of the coastal power plants production and sea water desalting companies, but also the establishment of the correlative trade standard.