Global Solvability and Vanishing Shear Viscosity Limit of Planar Magnetohydrodynamic Equations with Large Initial Data

2013/11/17 by Xulong Qin, Tong Yang, Qin, Xulong +5
Mathematics · #35B40 #35B45 #35L65 #76N10 #76W05 #76X05 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B40 #msc:35B45 #msc:35L65 #msc:76N10 #msc:76W05 #msc:76X05

paper · pdf · doi:10.48550/arxiv.1311.4106

This paper has been withdrawn by the author due to a serious gap

arxiv created 2013/12/02 · arxiv updated 2013/12/03

Abstract

By observing a new relation between the magnetic pressure and the hydrodynamic pressure, global existence of classical solution to the full perfect MHD equations with large data is established, in particular including the case when all the viscosity, heat conductivity and diffusivity coefficients are constant. This can be viewed as an analog of the classical work by Kazhikhov-Shelukhin for the Navier-Stokes equations to the MHD equations. In addition, the vanishing shear viscosity limit is proved.

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