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.

Thermal diffusion in the two-component fluid Bénard problem

Physica ◽  
1973 ◽  
Vol 64 (3) ◽  
pp. 481-496 ◽  
Author(s):  
J.C. Legros ◽  
P. Poty ◽  
G. Thomaes
Keyword(s):  
Thermal Diffusion ◽  
Two Component ◽  
Bénard Problem ◽  
Benard Problem

Global regularity for the micropolar Rayleigh-Bénard problem with only velocity dissipation

2021 ◽  
pp. 1-30
Author(s):  
Lihua Deng ◽  
Haifeng Shang
Keyword(s):  
Global Regularity ◽  
Special Structure ◽  
Regularity Of Solutions ◽  
Energy Methods ◽  
Regularity Problem ◽  
Interpolation Inequalities ◽  
Fourier Frequency ◽  
Bénard Problem ◽  
Benard Problem ◽  
Rayleigh Benard

This paper is concerned with the global regularity problem on the micropolar Rayleigh-Bénard problem with only velocity dissipation in $\mathbb {R}^{d}$ with $d=2\ or\ 3$ . By fully exploiting the special structure of the system, introducing two combined quantities and using the technique of Littlewood-Paley decomposition, we establish the global regularity of solutions to this system in $\mathbb {R}^{2}$ . Moreover, we obtain the global regularity for fractional hyperviscosity case in $\mathbb {R}^{3}$ by employing various techniques including energy methods, the regularization of generalized heat operators on the Fourier frequency localized functions and logarithmic Sobolev interpolation inequalities.

Global regularity for the 2D liquid crystal model with mixed partial viscosity

2015 ◽  
Vol 13 (02) ◽  
pp. 185-200 ◽  
Author(s):  
Jishan Fan ◽  
Faris Saeed Alzahrani ◽  
Tasawar Hayat ◽  
Gen Nakamura ◽  
Yong Zhou
Keyword(s):  
Liquid Crystal ◽  
Global Existence ◽  
Global Regularity ◽  
Strong Solutions ◽  
Regularity Criteria ◽  
Crystal Model

This paper proves the global existence of strong solutions of the 2D liquid crystal model when ν1= k2= 0, ν2= k1= 1 or ν1= k2= 1, ν2= k1= 0. We also prove some regularity criteria when ν1= k1= 1, ν2= k2= 0 or ν1= k1= 0, ν2= k2= 1.

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