Approximations to Isentropic Planar Magneto-Hydrodynamics Equations by Relaxed Euler-Type Systems |
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Authors: | Yachun LI · Zhaoyang SHANG · Chenmu WANG · Liang ZHAO |
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Affiliation: | School of Mathematical Sciences, CMA-Shanghai, MOE-LSC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240, China.;School of Finance, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, China;
School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China.;School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China; School of
Mathematical Sciences, Harbin Engineering University, Harbin 150001, China.; Mathematical Modelling & Data Analytics Center, Oxford Suzhou Centre for Advanced Research,
Suzhou 215123, Jiangsu, China. |
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Abstract: | 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 Amp`ere 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. |
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Keywords: | Planar MHD equations Relaxation limits Global convergence Stream
function |
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