In this paper, we consider with the large time behavior of solutions of the Cauchy problem to the one-dimensional compressible micropolar fluid model, where the far field states are prescribed. When the corresponding ...In this paper, we consider with the large time behavior of solutions of the Cauchy problem to the one-dimensional compressible micropolar fluid model, where the far field states are prescribed. When the corresponding Riemann problem for the Euler system admits the solution consisting of contact discontinuity and rarefaction waves, it is shown that the combination wave corresponding to the contact discontinuity, with rarefaction waves is asymptotically stable provided that the strength of the combination wave and the initial perturbation are suitably small. This result is proved by using elementary L2-energy methods.展开更多
We study the large-time asymptotics of solutions toward the weak rarefaction wave of the quasineutral Euler system for a two-fluid plasma model in the presence of diffusions of velocity and temperature under small per...We study the large-time asymptotics of solutions toward the weak rarefaction wave of the quasineutral Euler system for a two-fluid plasma model in the presence of diffusions of velocity and temperature under small perturbations of initial data and also under an extra assumption θ_i,+/θ_e,+=θ_i,-/θ_e,-≥m_i/2m_e,namely, the ratio of the thermal speeds of ions and electrons at both far fields is not less than one half. Meanwhile,we obtain the global existence of solutions based on energy method.展开更多
The paper is concerned with time-asymptotic behavior of solution near a local Maxwellian with rarefaction wave to a fluid-particle model described by the Vlasov-Fokker-Planck equation coupled with the compressible and...The paper is concerned with time-asymptotic behavior of solution near a local Maxwellian with rarefaction wave to a fluid-particle model described by the Vlasov-Fokker-Planck equation coupled with the compressible and inviscid fluid by Euler-Poisson equations through the relaxation drag frictions,Vlasov forces between the macroscopic and microscopic momentums and the electrostatic potential forces.Precisely,based on a new micro-macro decomposition around the local Maxwellian to the kinetic part of the fluid-particle coupled system,which was first developed in[16],we show the time-asymptotically nonlinear stability of rarefaction wave to the one-dimensional compressible inviscid Euler equations coupled with both the Vlasov-Fokker-Planck equation and Poisson equation.展开更多
The finite volume wave propagation method and the finite element RungeKutta discontinuous Galerkin(RKDG)method are studied for applications to balance laws describing plasma fluids.The plasma fluid equations explored ...The finite volume wave propagation method and the finite element RungeKutta discontinuous Galerkin(RKDG)method are studied for applications to balance laws describing plasma fluids.The plasma fluid equations explored are dispersive and not dissipative.The physical dispersion introduced through the source terms leads to the wide variety of plasma waves.The dispersive nature of the plasma fluid equations explored separates the work in this paper from previous publications.The linearized Euler equations with dispersive source terms are used as a model equation system to compare the wave propagation and RKDG methods.The numerical methods are then studied for applications of the full two-fluid plasma equations.The two-fluid equations describe the self-consistent evolution of electron and ion fluids in the presence of electromagnetic fields.It is found that the wave propagation method,when run at a CFL number of 1,is more accurate for equation systems that do not have disparate characteristic speeds.However,if the oscillation frequency is large compared to the frequency of information propagation,source splitting in the wave propagation method may cause phase errors.The Runge-Kutta discontinuous Galerkin method provides more accurate results for problems near steady-state as well as problems with disparate characteristic speeds when using higher spatial orders.展开更多
文摘In this paper, we consider with the large time behavior of solutions of the Cauchy problem to the one-dimensional compressible micropolar fluid model, where the far field states are prescribed. When the corresponding Riemann problem for the Euler system admits the solution consisting of contact discontinuity and rarefaction waves, it is shown that the combination wave corresponding to the contact discontinuity, with rarefaction waves is asymptotically stable provided that the strength of the combination wave and the initial perturbation are suitably small. This result is proved by using elementary L2-energy methods.
基金supported by the General Research Fund from Research Grants Council of Hong Kong(Grant No.400912)National Natural Science Foundation of China(Grant Nos.11101188+1 种基金11471142and 11331005)the Program for Changjiang Scholars and Innovative Research Team in University(Grant No.IRT13066)
文摘We study the large-time asymptotics of solutions toward the weak rarefaction wave of the quasineutral Euler system for a two-fluid plasma model in the presence of diffusions of velocity and temperature under small perturbations of initial data and also under an extra assumption θ_i,+/θ_e,+=θ_i,-/θ_e,-≥m_i/2m_e,namely, the ratio of the thermal speeds of ions and electrons at both far fields is not less than one half. Meanwhile,we obtain the global existence of solutions based on energy method.
基金supported by the NNSFC grant No.11971044partially supported by NNSFC grants No.11671385 and 11688101CAS Interdisciplinary Innovation Team
文摘The paper is concerned with time-asymptotic behavior of solution near a local Maxwellian with rarefaction wave to a fluid-particle model described by the Vlasov-Fokker-Planck equation coupled with the compressible and inviscid fluid by Euler-Poisson equations through the relaxation drag frictions,Vlasov forces between the macroscopic and microscopic momentums and the electrostatic potential forces.Precisely,based on a new micro-macro decomposition around the local Maxwellian to the kinetic part of the fluid-particle coupled system,which was first developed in[16],we show the time-asymptotically nonlinear stability of rarefaction wave to the one-dimensional compressible inviscid Euler equations coupled with both the Vlasov-Fokker-Planck equation and Poisson equation.
文摘The finite volume wave propagation method and the finite element RungeKutta discontinuous Galerkin(RKDG)method are studied for applications to balance laws describing plasma fluids.The plasma fluid equations explored are dispersive and not dissipative.The physical dispersion introduced through the source terms leads to the wide variety of plasma waves.The dispersive nature of the plasma fluid equations explored separates the work in this paper from previous publications.The linearized Euler equations with dispersive source terms are used as a model equation system to compare the wave propagation and RKDG methods.The numerical methods are then studied for applications of the full two-fluid plasma equations.The two-fluid equations describe the self-consistent evolution of electron and ion fluids in the presence of electromagnetic fields.It is found that the wave propagation method,when run at a CFL number of 1,is more accurate for equation systems that do not have disparate characteristic speeds.However,if the oscillation frequency is large compared to the frequency of information propagation,source splitting in the wave propagation method may cause phase errors.The Runge-Kutta discontinuous Galerkin method provides more accurate results for problems near steady-state as well as problems with disparate characteristic speeds when using higher spatial orders.
