Electron. J. Differential Equations, Vol. 2020 (2020), No. 11, pp. 1-16.

Free boundary value problem for compressible magnetohydrodynamic equations

Huihui Kong, Ruxu Lian

In this article we consider a free boundary value problem for barotropic compressible magnetohydrodynamic equations with density-dependent viscosity coefficients. Under certain assumptions imposed on the initial data, there exists a unique global strong solution which is strictly positive after a finite time. Furthermore, the free boundaries propagate along the particle path and the domain expands outwards at an algebraic rate.

Submitted September 25, 2019. Published January 23, 2020.
Math Subject Classifications: 35A01, 35R35, 35Q35.
Key Words: Magnetohydrodynamic equations; free boundary value problem; density-dependent viscosity coefficient; strong solution.

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Huihui Kong
School of Mathematics and Physics
University of Science and Technology Beijing Beijing 100083, China
email: konghuihuiking@126.com
Ruxu Lian
College of Mathematics and Information Science
North China University of Water Resources and Electric Power
Zhengzhou 450011, China
email: lianruxu@mail.iap.ac.cn

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