scholarly journals Finite energy weak solutions of 2d Boussinesq equations with diffusive temperature

2020 ◽  
Vol 40 (6) ◽  
pp. 3737-3765
Author(s):  
Tianwen Luo ◽  
◽  
Tao Tao ◽  
Liqun Zhang ◽  
◽  
...  
Keyword(s):  
Weak Solutions ◽  
Boussinesq Equations ◽  
Finite Energy ◽  
2D Boussinesq Equations

scholarly journals On the asymptotic stability of stratified solutions for the 2D Boussinesq equations with a velocity damping term

2019 ◽  
Vol 29 (07) ◽  
pp. 1227-1277 ◽  
Author(s):  
Ángel Castro ◽  
Diego Córdoba ◽  
Daniel Lear
Keyword(s):  
Asymptotic Stability ◽  
Boussinesq Equations ◽  
Boussinesq Approximation ◽  
Damping Term ◽  
Temperature Variations ◽  
Strip Domain ◽  
2D Boussinesq Equations

We consider the 2D Boussinesq equations with a velocity damping term in a strip domain, with impermeable walls. In this physical scenario, where the Boussinesq approximation is accurate when density or temperature variations are small, our main result is the asymptotic stability for a specific type of perturbations of a stratified solution.

scholarly journals Blow-Up Criterion of Weak Solutions for the 3D Boussinesq Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Zhaohui Dai ◽  
Xiaosong Wang ◽  
Lingrui Zhang ◽  
Wei Hou
Keyword(s):  
Weak Solutions ◽  
Blow Up ◽  
Three Dimensional ◽  
Boussinesq Equations ◽  
Interpolation Inequality ◽  
Embedding Theorem ◽  
The Earth ◽  
The Cauchy Problem ◽  
Homogeneous Besov Space ◽  
Blow Up Criterion

The Boussinesq equations describe the three-dimensional incompressible fluid moving under the gravity and the earth rotation which come from atmospheric or oceanographic turbulence where rotation and stratification play an important role. In this paper, we investigate the Cauchy problem of the three-dimensional incompressible Boussinesq equations. By commutator estimate, some interpolation inequality, and embedding theorem, we establish a blow-up criterion of weak solutions in terms of the pressurepin the homogeneous Besov spaceḂ∞,∞0.

scholarly journals The 2D Boussinesq equations with vertical viscosity and vertical diffusivity

2010 ◽  
Vol 249 (5) ◽  
pp. 1078-1088 ◽  
Author(s):  
Dhanapati Adhikari ◽  
Chongsheng Cao ◽  
Jiahong Wu
Keyword(s):  
Boussinesq Equations ◽  
Vertical Diffusivity ◽  
2D Boussinesq Equations
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