文献类型：期刊文献

中文题名：Global Existence and Optimal Decay Rate of the Compressible Magnetohydrodynamic Equation with Potential Force

英文题名：Global Existence and Optimal Decay Rate of the Compressible Magnetohydrodynamic Equation with Potential Force

作者：YE Lin[1];LI Yeping[1]

机构：[1]Department of Mathematics,East China University of Science and Technology

年份：2018

卷号：23

期号：4

起止页码：309

中文期刊名：Wuhan University Journal of Natural Sciences

外文期刊名：武汉大学学报（自然科学英文版）

收录：CSTPCD;;Scopus;CSCD:【CSCD2017_2018】；

基金：Supported by the National Natural Science Foundation of China(11671134)

语种：英文

中文关键词：magnetohydrodynamic equations;stationary solution;smooth solutions;energy estimate;optimal decay rate

外文关键词：magnetohydrodynamic equations;stationary solution;smooth solutions;energy estimate;optimal decay rate

摘要：In this paper, we consider the three dimensional compressible viscous magnetohydrodynamic equations（MHD） with the external potential force. We first derive the corresponding non-constant stationary solutions. Next, we show global wellposedness of the initial value problem for the three dimensional compressible viscous magnetohydrodynamic equations, provided that the initial data is close to the stationary solution. Finally, based on the elaborate energy estimates for the nonlinear system and L^p-L^q decay estimates of the linearized equation, we show the optimal convergence rates of the solution in L^q-norm with 2≤q≤6 and its first derivative in L^2-norm when the initial perturbation is bounded in L^p-norm with 1≤p〈6/5.
In this paper, we consider the three dimensional compressible viscous magnetohydrodynamic equations（MHD） with the external potential force. We first derive the corresponding non-constant stationary solutions. Next, we show global wellposedness of the initial value problem for the three dimensional compressible viscous magnetohydrodynamic equations, provided that the initial data is close to the stationary solution. Finally, based on the elaborate energy estimates for the nonlinear system and L^p-L^q decay estimates of the linearized equation, we show the optimal convergence rates of the solution in L^q-norm with 2≤q≤6 and its first derivative in L^2-norm when the initial perturbation is bounded in L^p-norm with 1≤p〈6/5.