Approximations to Isentropic Planar Magneto-Hydrodynamics Equations by Relaxed Euler-Type Systems

作     者：Yachun LI Zhaoyang SHANG Chenmu WANG Liang ZHAO Yachun LI;Zhaoyang SHANG;Chenmu WANG;Liang ZHAO

作者机构：School of Mathematical SciencesCMA-ShanghaiMOE-LSC and SHL-MACShanghai Jiao Tong UniversityShanghai 200240China School of FinanceShanghai Lixin University of Accounting and FinanceShanghai 201209China School of Mathematical SciencesShanghai Jiao Tong UniversityShanghai 200240China School of Mathematical SciencesHarbin Engineering UniversityHarbin 150001China Mathematical Modelling&Data Analytics CenterOxford Suzhou Centre for Advanced ResearchSuzhou 215123JiangsuChina 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2024年第45卷第3期

页      面：413-440页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the National Natural Science Foundation of China(Nos.12161141004,12371221,11831011,12301277) the Fundamental Research Funds for the Central Universities and Shanghai Frontiers Science Center of Modern Analysis and the Postdoctoral Science Foundation of China(No.2021M692089) 

主　　题：Planar MHD equations Relaxation limits Global convergence Stream function 

摘      要：In this paper, the authors consider an approximation to the isentropic planar Magneto-hydrodynamics(MHD for short) equations by a kind of relaxed Euler-type system. The approximation is based on the generalization of the Maxwell law for nonNewtonian fluids together with the Maxwell correction for the Ampe`re law, hence the approximate system becomes a first-order quasilinear symmetrizable hyperbolic systems with partial dissipation. They establish the global-in-time smooth solutions to the approximate Euler-type equations in a small neighbourhood of constant equilibrium states and obtain the global-in-time convergence towards the isentropic planar MHD equations. In addition, they also establish the global-in-time error estimates of the limit based on stream function techniques and energy estimates for error variables.