Related papers: Existence and uniqueness results for the Boussines…
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…
We study the global existence issue for the two-dimensional Boussinesq system with horizontal viscosity in only one equation. We first examine the case where the Navier-Stokes equation with no vertical viscosity is coupled with a transport…
This paper is devoted to the global existence and uniqueness results for the three-dimensional Boussinesq system with axisymmetric initial data $v^{0}{\in}B_{2,1}^{5/2}(\RR^3)$ and$ ${\rho}^{0}{\in}B_{2,1}^{1/2}(\RR^3)\cap L^{p}(\RR^3)$…
The contribution of this paper will be focused on the global existence and uniqueness topic in three-dimensional case of the axisymmetric viscous Boussinesq system in critical Lebesgue spaces. We aim at deriving analogous results for the…
In this paper we study the Cauchy problem for the generalized Boussinesq equation with initial data in modulation spaces $M^{s}_{p^\prime,q}(\mathbb{R}^n),$ $n\geq 1.$ After a decomposition of the Boussinesq equation in a $2\times…
The two-dimensional (2D) incompressible Euler equations have been thoroughly investigated and the resolution of the global (in time) existence and uniqueness issue is currently in a satisfactory status. In contrast, the global regularity…
In this paper we deal with the long time existence for the Cauchy problem associated to some asymptotic models for long wave, small amplitude gravity surface waves. We generalize some of the results that can be found in the literature…
We establish global existence and uniqueness theorems for the two-dimensional non-diffusive Boussinesq system with viscosity only in the horizontal direction, which arises in Ocean dynamics. This work improves the global well-posedness…
We study the global well-posedness of a two-dimensional Boussinesq system which couples the incompressible Euler equation for the velocity and a transport equation with fractional diffusion of type $|\DD|^{\alpha}$ for the temperature. We…
This paper deals with stability and the large-time decay to any given global smooth solutions of the 3D density-dependent incompressible Boussinesq system. The decay rate for solutions of the corresponding Cauchy problem is obtained in this…
We study the Cauchy problem for the Schr\"odinger-improved Boussinesq system in a two dimensional domain. Under natural assumptions on the data without smallness, we prove the existence and uniqueness of global strong solutions. Moreover,…
The global regularity problem for the Boussinesq system is a well known open problem in mathematical fluid dynamics. As a follow up to our work \cite{EJSI}, we give examples of finite-energy and Lipschitz continuous velocity field and…
This paper is about the dynamics of non-diffusive temperature fronts evolving by the incompressible viscous Boussinesq system in $\mathbb{R}^3$. We provide local in time existence results for initial data of arbitrary size. Furthermore, we…
Here we investigate the so-called temperature patch problem for the incompressible Boussinesq system with partial viscosity, in the whole space $\mathbb{R}^N$ $(N \geq 2)$, where the initial temperature is the characteristic function of…
The Boussinesq-Peregrine system is derived from the water waves system in presence of topographic variation under the hypothesis of shallowness and small amplitude regime. The system becomes significantly simpler (at least in the…
In this paper, we consider the viscous, incompressible, nonlinear Boussinesq system in two and three spatial dimension. We study the existence and regularity of solutions to the Boussinesq system with nonhomogeneous boundary conditions for…
This paper is concerned with a two dimensional Whitham-Boussinesq system modelling surface waves of an inviscid incompressible fluid layer. We prove that the associated Cauchy problem is well-posed for initial data of low regularity, with…
Considered herein is the global existence of weak, strong solutions and Rayleigh-Taylor (RT) instability for 2D semi-dissipative Boussinesq equations in an infinite strip domain $\Omega_{\infty}$ subject to Navier boundary conditions with…
In this paper we consider the Cauchy problem for 2D viscous shallow water system in Besov spaces. We firstly prove the local well-posedness of this problem in $B^s_{p,r}(\mathbb{R}^2)$, $s>max\{1,\frac{2}{p}\}$, $1\leq p,r\leq \infty$ by…
We prove local-in-time existence and uniqueness of an inviscid Boussinesq-type system. We assume the density equation contains nonzero diffusion and that our initial vorticity and density belong to a space of borderline Besov type.