Uniform global strong solutions of the 2D magnetic Bénard problem in a bounded domain

2018 ◽  
Vol 86 ◽  
pp. 166-172
Author(s):  
Jishan Fan ◽  
Dan Liu ◽  
Yong Zhou
Keyword(s):  
Bounded Domain ◽  
Strong Solutions ◽  
Bénard Problem ◽  
Benard Problem ◽  
Global Strong Solutions

scholarly journals Global Well-Posedness for the d -Dimensional Magnetic Bénard Problem without Thermal Diffusion

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Yinhong Cao
Keyword(s):  
Global Existence ◽  
Thermal Diffusion ◽  
Energy Method ◽  
Global Regularity ◽  
Strong Solutions ◽  
Minimal Amount ◽  
Well Posedness ◽  
Bénard Problem ◽  
Benard Problem

This paper focuses on the global existence of strong solutions to the magnetic Bénard problem with fractional dissipation and without thermal diffusion in ℝ d with d ≥ 3 . By using the energy method and the regularization of generalized heat operators, we obtain the global regularity for this model under minimal amount dissipation.

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 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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