Global well-posedness to the Cauchy problem of 2D inhomogeneous incompressible magnetic Bénard equations with large initial data and vacuum

Zhongying Liu; Zhongying Liu

doi:10.3934/math.2021701

AIMS Mathematics

2021, Volume 6, Issue 11: 12085-12103. doi: 10.3934/math.2021701

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Global well-posedness to the Cauchy problem of 2D inhomogeneous incompressible magnetic Bénard equations with large initial data and vacuum

Zhongying Liu ^,

College of Mathematics, Changchun Normal University, Changchun 130032, China

Received: 19 June 2021 Accepted: 17 August 2021 Published: 19 August 2021
MSC : 35Q35, 35B65, 76D03

In this paper, we are concerned with the Cauchy problem of inhomogeneous incompressible magnetic Bénard equations with vacuum as far-field density in $ \Bbb R^2 $. We prove that if the initial density and magnetic field decay not too slowly at infinity, the system admits a unique global strong solution. Note that the initial data can be arbitrarily large and the initial density can contain vacuum states and even has compact support. Moreover, we extend the result of [16, 17] to the global one.
- magnetic Bénard equations,
- global solution,
- large initial data,
- vacuum
Citation: Zhongying Liu. Global well-posedness to the Cauchy problem of 2D inhomogeneous incompressible magnetic Bénard equations with large initial data and vacuum[J]. AIMS Mathematics, 2021, 6(11): 12085-12103. doi: 10.3934/math.2021701

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Abstract

In this paper, we are concerned with the Cauchy problem of inhomogeneous incompressible magnetic Bénard equations with vacuum as far-field density in $ \Bbb R^2 $. We prove that if the initial density and magnetic field decay not too slowly at infinity, the system admits a unique global strong solution. Note that the initial data can be arbitrarily large and the initial density can contain vacuum states and even has compact support. Moreover, we extend the result of [16, 17] to the global one.

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