Singularity formation to the two-dimensional non-barotropic non-resistive magnetohydrodynamic equations with zero heat conduction in a bounded domain

Xin Zhong

doi:10.3934/dcdsb.2019209

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2020, Volume 25, Issue 3: 1083-1096. Doi: 10.3934/dcdsb.2019209

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Singularity formation to the two-dimensional non-barotropic non-resistive magnetohydrodynamic equations with zero heat conduction in a bounded domain

Xin Zhong

School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Received: September 30, 2018

Early access: September 2019

Published: March 2020

Supported by Fundamental Research Funds for the Central Universities (No. XDJK2019B031), Natural Science Foundation of Chongqing (No. cstc2018jcyjAX0049), the Postdoctoral Science Foundation of Chongqing (No. xm2017015), and China Postdoctoral Science Foundation (Nos. 2018T110936, 2017M610579)

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Abstract

We are concerned with the singularity formation of strong solutions to the two-dimensional (2D) non-barotropic non-resistive compressible magnetohydrodynamic equations with zero heat conduction in a bounded domain. It is showed that the strong solution exists globally if the density and the magnetic field as well as the pressure are bounded from above. Our method relies on critical Sobolev inequalities of logarithmic type.

Keywords:

Non-resistive compressible magnetohydrodynamic equations,
zero heat conduction,
blow-up criterion.

Mathematics Subject Classification: 76W05, 35B65.

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