Global Strong Solution of Nonhomogeneous Bénard System with Large Initial Data and Vacuum in a Bounded Domain

2021 ◽  
Vol 40 (2) ◽  
pp. 153-166 ◽  
Author(s):  
Xin Zhong
Keyword(s):  
Initial Data ◽  
Strong Solution ◽  
Bounded Domain ◽  
Large Initial Data ◽  
Global Strong Solution ◽  
Bénard System

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

2021 ◽  
Vol 6 (11) ◽  
pp. 12085-12103
Author(s):  
Zhongying Liu ◽  
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Initial Density ◽  
Well Posedness ◽  
Far Field ◽  
Large Initial Data ◽  
Global Strong Solution ◽  
Vacuum States ◽  
The Cauchy Problem ◽  
Field Decay

<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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