Global Strong Solutions of the 2D Density-Dependent Incompressible Magnetic Bénard Problem

Fan, Jishan; Wang, Handong; Zhou, Yong

doi:10.1007/s40840-020-01065-9

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2021

2022

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“…We start with the local existence and uniqueness of strong solution to the problem (1.1)-(1.3) with initial data satisfying (1.5), whose proof can be performed by using standard procedures as in [21,7] Lemma 2.1. Assume that the initial data (ρ 0 , u 0 , θ 0 , b 0 ) satisfies (1.5).…”

Section: Preliminariesmentioning

confidence: 99%

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

Liu

2021

MATH

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<abstract><p>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.</p></abstract>

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Section: Preliminariesmentioning

confidence: 99%