Global well-posedness for the 2D MHD-Boussinesq system with temperature-dependent diffusion

2020 ◽  
Vol 106 ◽  
pp. 106399 ◽  
Author(s):  
Yanghai Yu ◽  
Mingwen Fei
Keyword(s):  
Boussinesq System ◽  
Well Posedness ◽  
Temperature Dependent

Global Well-Posedness and Convergence Results for the 3D-Regularized Boussinesq System

2012 ◽  
Vol 64 (6) ◽  
pp. 1415-1435 ◽  
Author(s):  
Ridha Selmi
Keyword(s):  
Existence And Uniqueness ◽  
Analytical Study ◽  
Approximation Scheme ◽  
Boussinesq System ◽  
Well Posedness ◽  
Energy Methods ◽  
Unique Weak Solution ◽  
Frequency Space ◽  
Convergence Results ◽  
Fourier Theory

Abstract Analytical study of the regularization of the Boussinesq systemis performed in frequency space using Fourier theory. Existence and uniqueness of weak solutions with minimum regularity requirement are proved. Convergence results of the unique weak solution of the regularized Boussinesq system to a weak Leray-Hopf solution of the Boussinesq system are established as the regularizing parameter α vanishes. The proofs are done in the frequency space and use energy methods, the Arselà-Ascoli compactness theorem and a Friedrichs-like approximation scheme.

scholarly journals On the well-posedness and large-time behavior of higher order Boussinesq system

Nonlinearity ◽  
2019 ◽  
Vol 32 (5) ◽  
pp. 1852-1881 ◽  
Author(s):  
Roberto A Capistrano-Filho ◽  
Fernando A Gallego ◽  
Ademir F Pazoto
Keyword(s):  
Large Time ◽  
Large Time Behavior ◽  
Higher Order ◽  
Boussinesq System ◽  
Well Posedness ◽  
Time Behavior

scholarly journals On the local well-posedness of a Benjamin-Ono-Boussinesq system

2005 ◽  
Vol 2005 (22) ◽  
pp. 3609-3630
Author(s):  
Ruying Xue
Keyword(s):  
Sobolev Space ◽  
Boussinesq System ◽  
Well Posedness ◽  
Well Posed

Consider a Benjamin-Ono-Boussinesq systemηt+ux+auxxx+(uη)x=0,ut+ηx+uux+cηxxx−duxxt=0, wherea,c, anddare constants satisfyinga=c>0,d>0ora<0,c<0,d>0. We prove that this system is locally well posed in Sobolev spaceHs(ℝ)×Hs+1(ℝ), withs>1/4.

scholarly journals On the Nonlinear Stability and Instability of the Boussinesq System for Magnetohydrodynamics Convection

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1049
Author(s):  
Dongfen Bian
Keyword(s):  
Equilibrium State ◽  
Nonlinear Stability ◽  
Lower Boundary ◽  
Equilibrium Temperature ◽  
Mhd Equations ◽  
Boussinesq System ◽  
Fluid Viscosity ◽  
Asymptotically Stable ◽  
Temperature Dependent ◽  
Stability And Instability

This paper is concerned with the nonlinear stability and instability of the two-dimensional (2D) Boussinesq-MHD equations around the equilibrium state ( u ¯ = 0 , B ¯ = 0 , θ ¯ = θ 0 ( y ) ) with the temperature-dependent fluid viscosity, thermal diffusivity and electrical conductivity in a channel. We prove that if a + ≥ a − , and d 2 d y 2 κ ( θ 0 ( y ) ) ≤ 0 or 0 < d 2 d y 2 κ ( θ 0 ( y ) ) ≤ β 0 , with β 0 > 0 small enough constant, and then this equilibrium state is nonlinearly asymptotically stable, and if a + < a − , this equilibrium state is nonlinearly unstable. Here, a + and a − are the values of the equilibrium temperature θ 0 ( y ) on the upper and lower boundary.

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