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

作　　者：Yachun LI Zhaoyang SHANG Chenmu WANG Liang ZHAO 

机构地区：[1]School of Mathematical Sciences,CMA-Shanghai,MOE-LSC and SHL-MAC,Shanghai Jiao Tong University,Shanghai 200240,China [2]School of Finance,Shanghai Lixin University of Accounting and Finance,Shanghai 201209,China [3]School of Mathematical Sciences,Shanghai Jiao Tong University,Shanghai 200240,China [4]School of Mathematical Sciences,Harbin Engineering University,Harbin 150001,China [5]Mathematical Modelling&Data Analytics Center,Oxford Suzhou Centre for Advanced Research,Suzhou 215123,Jiangsu,China

出　　处：《Chinese Annals of Mathematics,Series B》2024年第3期413-440,共28页数学年刊（B辑英文版）

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).

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.

关 键 词：Planar MHD equations Relaxation limits Global convergence Stream function 

分 类 号：O361.3[理学—流体力学]