We consider a non-isentropic Euler-Poisson system with two small parameters arising in the modeling of unmagnetized plasmas and semiconductors.On the basis of the energy estimates and the compactness theorem,the unifo...We consider a non-isentropic Euler-Poisson system with two small parameters arising in the modeling of unmagnetized plasmas and semiconductors.On the basis of the energy estimates and the compactness theorem,the uniform global existence of the solutions and the combined quasi-neutral and zero-electron-mass limit of the system are proved when the initial data are close to the constant equilibrium state.In particular,the limit is rigorously justified as the two parameters tend to zero independently.展开更多
Consider the Cauchy problems for an n-dimensional nonlinear system of fluid dynamics equations. The main purpose of this paper is to improve the Fourier splitting method to accomplish the decay estimates with sharp ra...Consider the Cauchy problems for an n-dimensional nonlinear system of fluid dynamics equations. The main purpose of this paper is to improve the Fourier splitting method to accomplish the decay estimates with sharp rates of the global weak solutions of the Cauchy problems. We will couple togeth- er the elementary uniform energy estimates of the global weak solutions and a well known Gronwall＇s inequality to improve the Fourier splitting method. This method was initiated by Maria Schonbek in the 1980＇s to study the op- timal long time asymptotic behaviours of the global weak solutions of the nonlinear system of fluid dynamics equations. As applications, the decay esti- mates with sharp rates of the global weak solutions of the Cauchy problems for n-dimensional incompressible Navier-Stokes equations, for the n-dimensional magnetohydrodynamics equations and for many other very interesting nonlin- ear evolution equations with dissipations can be established.展开更多
基金partially supported by the ISFNSFC joint research program(11761141008)NSFC(12071044 and 12131007)the NSF of Jiangsu Province(BK20191296)。
文摘We consider a non-isentropic Euler-Poisson system with two small parameters arising in the modeling of unmagnetized plasmas and semiconductors.On the basis of the energy estimates and the compactness theorem,the uniform global existence of the solutions and the combined quasi-neutral and zero-electron-mass limit of the system are proved when the initial data are close to the constant equilibrium state.In particular,the limit is rigorously justified as the two parameters tend to zero independently.
文摘Consider the Cauchy problems for an n-dimensional nonlinear system of fluid dynamics equations. The main purpose of this paper is to improve the Fourier splitting method to accomplish the decay estimates with sharp rates of the global weak solutions of the Cauchy problems. We will couple togeth- er the elementary uniform energy estimates of the global weak solutions and a well known Gronwall＇s inequality to improve the Fourier splitting method. This method was initiated by Maria Schonbek in the 1980＇s to study the op- timal long time asymptotic behaviours of the global weak solutions of the nonlinear system of fluid dynamics equations. As applications, the decay esti- mates with sharp rates of the global weak solutions of the Cauchy problems for n-dimensional incompressible Navier-Stokes equations, for the n-dimensional magnetohydrodynamics equations and for many other very interesting nonlin- ear evolution equations with dissipations can be established.
