Related papers: Global Regularity for the Two-dimensional Boussine…

In this paper, we study the regularity criteria for the 3D Boussinesq equations in terms of one partial derivative of the velocity in Besov spaces. More precisely, it is proved that if the velocity $u$ holds $\int_{0}^{T}\| \partial_{3}…

As a continuation of the previous work [40], in this paper we focus on the Cauchy problem of the two-dimensional (2D) incompressible Boussinesq equations with fractional Laplacian dissipation. We give an elementary proof of the global…

The present paper is dedicated to the study of the global existence for the inviscid two-dimensional Boussinesq system. We focus on finite energy data with bounded vorticity and we find out that, under quite a natural additional assumption…

In this paper, we study the 3D regularized Boussinesq equations. The velocity equation is regularized \`a la Leray through a smoothing kernel of order $\alpha$ in the nonlinear term and a $\beta$-fractional Laplacian; we consider the…

In this paper, we deal with the global exact controllability to the trajectories of the Boussinesq system. We consider 2D and 3D smooth bounded domains. The velocity field of the fluid must satisfy a Navier slip-with-friction boundary…

We prove global regularity and study the infinite Prandtl number limit of temperature patches for the 2D non-diffusive Boussinesq system with dissipation in the full subcritical regime. The temperature satisfies a transport equation and the…

We investigate the asymptotic stability of solution to Boussinesq equations without thermal conduction with the initial data near a specific stationary solution in the three--dimensional domain $\Omega = \mathbb{R}^{2}\times (0,1)$. It is…

We establish global-posedness in time for the viscous Boussinesq equations in two dimensions of space with temperature-dependent diffusivity in the framework of a smooth vortex patch. We also provide the inviscid limit for velocity,…

In this paper we establish some regularity criteria for the 3D Boussinesq system with the temperature-dependent viscosity and thermal diffusivity. We also obtain some uniform estimates for the corresponding 2D case when the fluid viscosity…

In this paper, we consider the two-dimensional (2D) incompressible Boussinesq system with fractional Laplacian dissipation and thermal diffusion. Based on the previous works and some new observations, we show that the condition $1-\alpha…

In this paper we prove the global well-posedness of the two-dimensional Boussinesq system with zero viscosity for rough initial data.

In this paper, we investigate the global existence and uniqueness of strong solutions to 2D Boussinesq system with anisotropic thermal diffusion or anisotropic viscosity and with striated initial data. Using the key idea of Chemin to solve…

We consider an initial boundary value problem of the multi-dimensional Boussinesq equations in the absence of thermal diffusion with velocity damping or velocity diffusion under the stress free boundary condition in horizontally periodic…

This article studies the global regularity problem of the two-dimensional zero thermal diffusion tropical climate model with fractional dissipation, given by $(-\Delta)^{\alpha}u$ in the barotropic mode equation and by $(-\Delta)^{\beta}v$…

We address the well-posedness of the 2D (Euler)-Boussinesq equations with zero viscosity and positive diffusivity in the polygonal-like domains with Yudovich's type data, which gives a positive answer to part of the questions raised in 2011…

In this paper, we investigate the Cauchy problem for the tridimensional Boussinesq equations with horizontal dissipation. Under the assumption that the initial data is an axisymmetric without swirl, we prove the global well-posedness for…

In this paper we study the regularity properties of the "good" Boussinesq equation on the half line. We obtain local existence, uniqueness and continuous dependence on initial data in low-regularity spaces. Moreover we prove that the…

We establish long-time existence of smooth solutions to the 2D ideal Boussinesq equations and to the 2D non-homogeneous incompressible Euler equations for initial data consisting of small temperature perturbations, or small density…

For two dimensional inhomogeneous Navier-Stokes of incompressible flows, with the assumption that the viscosity depends on the density but with a positive lower bound, using a partial regularity approach, in particular some enhanced decay…

We study a three-dimensional Boussinesq-type temperature-velocity system on a bounded smooth domain $\mathcal D\subset\mathbb R^3$, where the velocity $u^\varepsilon$ solves the Navier-Stokes equations and the temperature…