Global well-posedness for the two dimensional compressible MHD equations with large data

Details Global well-posedness for the two dimensional compressible MHD equations with large data Global well-posedness for the two dimensional compressible MHD equations with large data

2012-04-25

arxiv.org/abs/1204.5608v1

Mathematics

Analysis of PDEs

43 pages

Scientific paper

In this paper we are concerned with the global well-posedness for the compressible MHD equations with large data. We show that if the shear viscosity $\mu$ is a positive constant and the bulk viscosity $\lambda$ is the power function of the density, that is, $\lambda(\rho)=\rho^{\beta}$ with $\beta>3$, then the two dimensional compressible MHD system with the periodic boundary conditions on the torus $\mathbb{T}^2$ have a unique global classical solution $(\rho, u,H)$. In this work we extended the results about compressible Navier-Stokes equations in \cite{Karzhikhov} to compressible MHD equations by applying several new techniques to overcome the coupling between velocity and magnetic field.

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