Stability near hydrostatic equilibrium to the 2D Boussinesq equations without thermal diffusion

L Tao, J Wu, K Zhao, X Zheng - Archive for Rational Mechanics and …, 2020‏ - Springer
This paper furthers our studies on the stability problem for perturbations near hydrostatic
equilibrium of the 2D Boussinesq equations without thermal diffusion and solves some of the …

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 …

Continuous data assimilation for the 2D Bénard convection through velocity measurements alone

A Farhat, MS Jolly, ES Titi - Physica D: Nonlinear Phenomena, 2015‏ - Elsevier
An algorithm for continuous data assimilation for the two-dimensional Bénard convection
problem is introduced and analyzed. It is inspired by the data assimilation algorithm …

Global well-posedness of the 2D Boussinesq equations with vertical dissipation

J Li, ES Titi - Archive for Rational Mechanics and Analysis, 2016‏ - Springer
We prove the global well-posedness of the two-dimensional Boussinesq equations with only
vertical dissipation. The initial data (u_0,\theta_0)(u 0, θ 0) are required to be only in the …

Small scale formation for the 2D Boussinesq equation

A Kiselev, J Park, Y Yao - arxiv preprint arxiv:2211.05070, 2022‏ - arxiv.org
We study the 2D incompressible Boussinesq equation without thermal diffusion, and aim to
construct rigorous examples of small scale formations as time goes to infinity. In the viscous …

[HTML][HTML] On the local well-posedness and a Prodi–Serrin-type regularity criterion of the three-dimensional MHD-Boussinesq system without thermal diffusion

A Larios, Y Pei - Journal of Differential Equations, 2017‏ - Elsevier
Abstract We prove a Prodi–Serrin-type global regularity condition for the three-dimensional
Magnetohydrodynamic-Boussinesq system (3D MHD-Boussinesq) without thermal diffusion …

Asymptotic stability of the 2D Boussinesq equations without thermal conduction

L Dong, Y Sun - Journal of Differential Equations, 2022‏ - Elsevier
The paper is concerned with asymptotic stability of certain stationary solution to Boussinesq
equations without thermal conduction in the infinite flat strip Ω= R×(0, 1). It is shown that the …

Persistence of regularity for the viscous Boussinesq equations with zero diffusivity

W Hu, I Kukavica, M Ziane - Asymptotic Analysis, 2015‏ - content.iospress.com
We address the global regularity for the 2D Boussinesq equations with positive viscosity and
zero diffusivity. We prove that for data (u 0, ρ 0) in H s× H s− 1, where 1< s< 2, the …

Partially dissipative 2D Boussinesq equations with Navier type boundary conditions

W Hu, Y Wang, J Wu, B **ao, J Yuan - Physica D: Nonlinear Phenomena, 2018‏ - Elsevier
This paper concerns itself with two systems of the 2D Boussinesq equations with partial
dissipation in bounded domains with the Navier type boundary conditions. We attempt to …

Global well-posedness and stability of the 2D Boussinesq equations with partial dissipation near a hydrostatic equilibrium

K Kang, J Lee, DD Nguyen - Journal of Differential Equations, 2024‏ - Elsevier
The paper is devoted to investigating the well-posedness, stability and large-time behavior
near the hydrostatic balance for the 2D Boussinesq equations with partial dissipation. More …