scholarly journals Uniform local well-posedness and regularity criterion for the density-dependent incompressible flow of liquid crystals

2014 ◽  
Vol 12 (7) ◽  
pp. 1185-1197
Author(s):  
Jishan Fan ◽  
Fucai Li
Keyword(s):  
Liquid Crystals ◽  
Incompressible Flow ◽  
Regularity Criterion ◽  
Well Posedness ◽  
Density Dependent

scholarly journals GLOBAL STRONG SOLUTIONS OF THE DENSITY-DEPENDENT INCOMPRESSIBLE MHD SYSTEM WITH ZERO RESISTIVITY IN A BOUNDED DOMAIN

2019 ◽  
Vol 24 (1) ◽  
pp. 95-104 ◽  
Author(s):  
Jishan Fan ◽  
Bessem Samet ◽  
Yong Zhou
Keyword(s):  
Bounded Domain ◽  
Initial Density ◽  
Strong Solutions ◽  
Regularity Criterion ◽  
Well Posedness ◽  
Density Dependent ◽  
Bootstrap Argument ◽  
Global Strong Solutions ◽  
Mhd System ◽  
Incompressible Mhd

In this paper, we first establish a regularity criterion for the strong solutions to the density-dependent incompressible MHD system with zero resistivity in a bounded domain. Then we use it and the bootstrap argument to prove the global well-posedness provided that the initial data u0 and b0 satisfy that (d-2)||∇u0 || L2+||b0||w1,p are sufficiently small with . We do not assume the positivity of initial density, it may vanish in an open subset (vacuum) of Ω.

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