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| Approximations to Isentropic Planar Magneto-Hydrodynamics Equations by Relaxed Euler-Type Systems |
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Citation： |
Yachun LI ·,Zhaoyang SHANG ·,Chenmu WANG ·,Liang ZHAO.Approximations to Isentropic Planar Magneto-Hydrodynamics Equations by Relaxed Euler-Type Systems[J].Chinese Annals of Mathematics B,2024,45(3):413~440 |
| Page view： 1095
Net amount： 777 |
Authors： |
Yachun LI ·; Zhaoyang SHANG ·;Chenmu WANG ·;Liang ZHAO |
Foundation： |
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) |
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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. |
Keywords： |
Planar MHD equations, Relaxation limits, Global convergence, Stream
function |
Classification： |
35B25, 35L45, 35K45, 76W05 |
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