One new blow-up criterion for the two-dimensional full compressible magnetohydrodynamic equations

Li Lu; Li Lu

doi:10.3934/math.2023810

AIMS Mathematics

2023, Volume 8, Issue 7: 15876-15891. doi: 10.3934/math.2023810

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Research article

One new blow-up criterion for the two-dimensional full compressible magnetohydrodynamic equations

Li Lu ^{1,2
,
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1.
School of Mathematics, East China University of Science and Technology, Shanghai 200237, China
2.
College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang 330063, Jiangxi, China

Received: 06 March 2023 Revised: 09 April 2023 Accepted: 12 April 2023 Published: 04 May 2023
MSC : 76W05, 35B44

This paper concerns the blow-up criterion for two-dimensional (2D) viscous, compressible, and heat conducting magnetohydrodynamic(MHD) flows. When the magnetic field $ H $ satisfies the perfect conducting boundary condition $ H\cdot n = \mbox{curl} H = 0 $, we prove that for the initial boundary value problem of the two-dimensional full compressible MHD flows with initial density allowed to vanish, the strong solution exists globally provided $ \|H\|_{L^\infty(0, T; \; L^b)}+\| {{\rm{div }}} u\|_{L^1(0, T; \; L^\infty)} < \infty $ for any $ b > 2 $.
- full compressible MHD equations,
- strong solution,
- blow-up criterion
Citation: Li Lu. One new blow-up criterion for the two-dimensional full compressible magnetohydrodynamic equations[J]. AIMS Mathematics, 2023, 8(7): 15876-15891. doi: 10.3934/math.2023810

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Abstract

This paper concerns the blow-up criterion for two-dimensional (2D) viscous, compressible, and heat conducting magnetohydrodynamic(MHD) flows. When the magnetic field $ H $ satisfies the perfect conducting boundary condition $ H\cdot n = \mbox{curl} H = 0 $, we prove that for the initial boundary value problem of the two-dimensional full compressible MHD flows with initial density allowed to vanish, the strong solution exists globally provided $ \|H\|_{L^\infty(0, T; \; L^b)}+\| {{\rm{div }}} u\|_{L^1(0, T; \; L^\infty)} < \infty $ for any $ b > 2 $.

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