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.

Global strong solutions of the MHD system with zero resistivity in a bounded domain

2018 ◽  
Vol 291 (17-18) ◽  
pp. 2557-2564
Author(s):  
Jishan Fan ◽  
Bessem Samet ◽  
Yong Zhou
Keyword(s):  
Bounded Domain ◽  
Strong Solutions ◽  
Global Strong Solutions ◽  
Mhd System

scholarly journals Global Strong Solution to the Density-Dependent 2-D Liquid Crystal Flows

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yong Zhou ◽  
Jishan Fan ◽  
Gen Nakamura
Keyword(s):  
Strong Solution ◽  
Initial Density ◽  
Regularity Criterion ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Density Dependent ◽  
Global Strong Solution ◽  
Dependent Flow ◽  
Density Dependent Flow ◽  
Initial Boundary Value

The initial-boundary value problem for the density-dependent flow of nematic crystals is studied in a 2-D bounded smooth domain. For the initial density away from vacuum, the existence and uniqueness is proved for the global strong solution with the large initial velocityu0and small∇d0. We also give a regularity criterion∇d∈Lp(0,T;Lq(Ω))  (2/q)+(2/p)=1, 2<q≤∞of the problem with the Dirichlet boundary conditionu=0,d=d0on∂Ω.

Strong solutions to the density-dependent incompressible Cahn–Hilliard–Navier–Stokes system

2019 ◽  
Vol 16 (04) ◽  
pp. 701-742 ◽  
Author(s):  
Xiaopeng Zhao
Keyword(s):  
Stokes System ◽  
Initial Density ◽  
Local Existence ◽  
Strong Solutions ◽  
Incompressible Fluids ◽  
Navier Stokes ◽  
Initial Value ◽  
Two Phase ◽  
Density Dependent ◽  
Local Existence And Uniqueness

We study the density-dependent incompressible Cahn–Hilliard–Navier–Stokes system, which describes a two-phase flow of two incompressible fluids with different densities. We establish the local existence and uniqueness of strong solutions to the initial value problem in a bounded domain, when the initial density function enjoys a positive lower bound.

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