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
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
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
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
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
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
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
基金Supported by National Natural Science Foundation of China(11271305)
文摘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.
文摘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.
基金supported by Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality(Grant No.PHR201006107)the Key Project of the Beijing Municipal Education Commission(Grant No.KZ201210028033)
文摘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.
基金supported by the NSFC (10871134),supported by the NSFC (10871134, 10771008)the NCET support of the Ministry of Education of China+1 种基金the Huo Ying Dong Fund (111033)the funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (PHR201006107)
文摘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.
基金supported by the NSFC (10871134)supported by the NSFC (10871134,10910401059)+1 种基金the funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (PHR201006107)supported by the General Research Fund of Hong Kong,City Univ.103108
文摘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.
基金supported partially by the NNSFC Grant(11371151)the Scientific Research Foundation of Graduate School of South China Normal University
文摘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.
基金Supported by the National Natural Science Foundation of China(No.10872004)
文摘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.
