Global regularity to the 3D Cauchy problem of inhomogeneous magnetic Bénard equations with vacuum

Wen Wang; Yang Zhang; Wen Wang; Yang Zhang

doi:10.3934/math.2023942

AIMS Mathematics

2023, Volume 8, Issue 8: 18528-18545. doi: 10.3934/math.2023942

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Research article

Global regularity to the 3D Cauchy problem of inhomogeneous magnetic Bénard equations with vacuum

Wen Wang ,
Yang Zhang ^,

School of Medical Information, Changchun University of Chinese Medicine, Changchun 130117, China

Received: 20 April 2023 Revised: 21 May 2023 Accepted: 26 May 2023 Published: 31 May 2023
MSC : 35Q35, 76D03, 76W05

This paper deals with the Cauchy problem of 3D inhomogeneous incompressible magnetic Bénard equations. Through some time-weighted a priori estimates, we prove the global existence of strong solution provided that the upper boundedness of initial density and initial magnetic field satisfy some smallness condition. Furthermore, we also obtain large time decay rates of the solution.
- inhomogeneous case,
- magnetic Bénard equations,
- global regularity,
- decay estimates
Citation: Wen Wang, Yang Zhang. Global regularity to the 3D Cauchy problem of inhomogeneous magnetic Bénard equations with vacuum[J]. AIMS Mathematics, 2023, 8(8): 18528-18545. doi: 10.3934/math.2023942

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Abstract

This paper deals with the Cauchy problem of 3D inhomogeneous incompressible magnetic Bénard equations. Through some time-weighted a priori estimates, we prove the global existence of strong solution provided that the upper boundedness of initial density and initial magnetic field satisfy some smallness condition. Furthermore, we also obtain large time decay rates of the solution.

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