ZERO KINEMATIC VISCOSITY-MAGNETIC DIFFUSION LIMIT OF THE INCOMPRESSIBLE VISCOUS MAGNETOHYDRODYNAMIC EQUATIONS WITH NAVIER BOUNDARY CONDITIONS

doi:10.1007/s10473-021-0507-4

Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (5): 1503-1536.doi: 10.1007/s10473-021-0507-4

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ZERO KINEMATIC VISCOSITY-MAGNETIC DIFFUSION LIMIT OF THE INCOMPRESSIBLE VISCOUS MAGNETOHYDRODYNAMIC EQUATIONS WITH NAVIER BOUNDARY CONDITIONS

Fucai LI¹, Zhipeng ZHANG^1,2

1. Department of Mathematics, Nanjing University, Nanjing 210093, China;
2. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

Received:2020-02-28 Revised:2021-05-13 Online:2021-10-25 Published:2021-10-21
Contact: Zhipeng ZHANG E-mail:zhangzhipeng@nju.edu.cn
Supported by:
Li was supported partially by NSFC (11671193, 11971234) and PAPD. Zhang was supported partially by the China Postdoctoral Science Foundation (2019M650581).

Abstract

Abstract: We investigate the uniform regularity and zero kinematic viscosity-magnetic diffusion limit for the incompressible viscous magnetohydrodynamic equations with the Navier boundary conditions on the velocity and perfectly conducting conditions on the magnetic field in a smooth bounded domain $\Omega\subset\mathbb{R}^3$. It is shown that there exists a unique strong solution to the incompressible viscous magnetohydrodynamic equations in a finite time interval which is independent of the viscosity coefficient and the magnetic diffusivity coefficient. The solution is uniformly bounded in a conormal Sobolev space and $W^{1,\infty}(\Omega)$ which allows us to take the zero kinematic viscosity-magnetic diffusion limit. Moreover, we also get the rates of convergence in $L^\infty(0,T; L^2)$, $L^\infty(0,T; W^{1,p})\,(2\leq p<\infty)$, and $L^\infty((0,T)\times \Omega)$ for some $T>0$.

Key words: incompressible viscous MHD equations, ideal incompressible MHD equations, Navier boundary conditions, zero kinematic viscosity-magnetic diffusion limit

CLC Number:

35Q30

Fucai LI, Zhipeng ZHANG. ZERO KINEMATIC VISCOSITY-MAGNETIC DIFFUSION LIMIT OF THE INCOMPRESSIBLE VISCOUS MAGNETOHYDRODYNAMIC EQUATIONS WITH NAVIER BOUNDARY CONDITIONS[J].Acta mathematica scientia,Series B, 2021, 41(5): 1503-1536.

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ZERO KINEMATIC VISCOSITY-MAGNETIC DIFFUSION LIMIT OF THE INCOMPRESSIBLE VISCOUS MAGNETOHYDRODYNAMIC EQUATIONS WITH NAVIER BOUNDARY CONDITIONS

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