Singularity formation to the 2D Cauchy problem of nonbarotropic magnetohydrodynamic equations without heat conductivity

Author:

Zhong Xin1

Affiliation:

1. School of Mathematics and Statistics Southwest University Chongqing People's Republic of China

Abstract

AbstractThe question of whether the two‐dimensional (2D) nonbarotropic compressible magnetohydrodynamic (MHD) equations with zero heat conduction can develop a finite‐time singularity from smooth initial data is a challenging open problem in fluid dynamics and mathematics. Such a problem is interesting in studying global well‐posedness of solutions. In this paper, we proved that, for the initial density allowing vacuum states, the strong solution exists globally if the density and the pressure are bounded from above. Our method relies on weighted energy estimates and a Hardy‐type inequality.

Funder

National Natural Science Foundation of China

Publisher

Wiley

Subject

General Mathematics

Reference33 articles.

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