Global regularity for the 2D Boussinesq equations with partial viscosity terms

D Chae - Advances in Mathematics, 2006 - Elsevier
In this paper, we prove the global in time regularity for the 2D Boussinesq system with either
the zero diffusivity or the zero viscosity. We also prove that as diffusivity (viscosity) tends to …

Global regularity for the two-dimensional anisotropic Boussinesq equations with vertical dissipation

C Cao, J Wu - Archive for Rational Mechanics and Analysis, 2013 - Springer
This paper establishes the global in time existence of classical solutions to the two-
dimensional anisotropic Boussinesq equations with vertical dissipation. When only vertical …

[HTML][HTML] A regularity criterion in weak spaces to Boussinesq equations

RP Agarwal, S Gala, MA Ragusa - Mathematics, 2020 - mdpi.com
A Regularity Criterion in Weak Spaces to Boussinesq Equations Next Article in Journal
Using a Fuzzy Inference System to Obtain Technological Tables for Electrical Discharge …

[HTML][HTML] Global well-posedness for the 2D Boussinesq system with anisotropic viscosity and without heat diffusion

A Larios, E Lunasin, ES Titi - Journal of Differential Equations, 2013 - Elsevier
We establish global existence and uniqueness theorems for the two-dimensional non-
diffusive Boussinesq system with anisotropic viscosity acting only in the horizontal direction …

Long time behavior of the two-dimensional Boussinesq equations without buoyancy diffusion

CR Doering, J Wu, K Zhao, X Zheng - Physica D: Nonlinear Phenomena, 2018 - Elsevier
We study the global well-posedness and stability/instability of perturbations near a special
type of hydrostatic equilibrium associated with the 2D Boussinesq equations without …

Nonlinear inviscid dam** and shear‐buoyancy instability in the two‐dimensional Boussinesq equations

J Bedrossian, R Bianchini, MC Zelati… - … on Pure and Applied …, 2023 - Wiley Online Library
We investigate the long‐time properties of the two‐dimensional inviscid Boussinesq
equations near a stably stratified Couette flow, for an initial Gevrey perturbation of size ε …

Logarithmically improved regularity criterion for the Boussinesq equations in Besov spaces with negative indices

S Gala, MA Ragusa - Applicable Analysis, 2016 - Taylor & Francis
Logarithmically improved regularity criterion for the Boussinesq equations in Besov spaces
with negative indices Page 1 Applicable Analysis, 2016 Vol. 95, No. 6, 1271–1279, http://dx.doi.org/10.1080/00036811.2015.1061122 …

Initial boundary value problem for two-dimensional viscous Boussinesq equations

MJ Lai, R Pan, K Zhao - Archive for rational mechanics and analysis, 2011 - Springer
We study the initial boundary value problem of two-dimensional viscous Boussinesq
equations over a bounded domain with smooth boundary. We show that the equations have …

Stability of the Couette flow for a 2D Boussinesq system without thermal diffusivity

N Masmoudi, B Said-Houari, W Zhao - Archive for Rational Mechanics and …, 2022 - Springer
In this paper, we prove the stability of the Couette flow for a 2D Navier–Stokes Boussinesq
system without thermal diffusivity for the initial perturbation in Gevrey- 1 s \documentclass[12pt]{minimal} …

Stability and exponential decay for the 2D anisotropic Boussinesq equations with horizontal dissipation

B Dong, J Wu, X Xu, N Zhu - Calculus of Variations and Partial Differential …, 2021 - Springer
The hydrostatic equilibrium is a prominent topic in fluid dynamics and astrophysics.
Understanding the stability of perturbations near the hydrostatic equilibrium of the …