相关论文: The stationary Boussinesq problem under singular f…
We study the nonhomogeneous Dirichlet problem for first order Hamilton-Jacobi equations associated with Tonelli Hamiltonians on a bounded domain $\Omega$ of $\R^n$ assuming the energy level to be supercritical. First, we show that the…
This paper is concerned with an inverse source problem for the three-dimensional Helmholtz equation by a single boundary measurement at a fixed frequency. We show the Lipschitz stability under the assumption that the source function 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 investigate the Cauchy problem for the three dimensional inviscid Boussinesq system in the periodic setting. For $1\le p\le \infty$, we show that the threshold regularity exponent for $L^p$-norm conservation of temperature…
In this paper we propose and analyse a new formulation and pointwise divergence-free mixed finite element methods for the numerical approximation of Darcy--Brinkman equations in vorticity--velocity--pressure form, coupled with a transport…
The three-dimensional incompressible Boussinesq system is one of the important equations in fluid dynamics. The system describes the motion of temperature-dependent incompressible flows. And the temperature naturally has diffusion.…
We are concerned with the so-called Boussinesq equations with partial viscosity. These equations consist of the ordinary incompressible Navier-Stokes equations with a forcing term which is transported {\it with no dissipation} by the…
In this paper, the boundary flex control problem of non stationary equation governing the coupled mass and heat flow of a viscous incompressible fluid in a generalized Boussinesq approximation by assuming that viscosity and heat…
To investigate the finite time singularity in three-dimensional (3D) Euler flows, the simplified model of 3D axisymmetric incompressible fluids (i.e., two-dimensional Boussinesq approximation equations) is studied numerically. The system…
In this paper, a generalized Boussinesq equation that couples the mass and heat flows in a viscous incompressible uid is considered. The kinematic viscosity and the heat conductivity are assumed to be dependent on the temperature. The…
We study the heat equation on time-dependent metric measure spaces (as well as the dual and the adjoint heat equation) and prove existence, uniqueness and regularity. Of particular interest are properties which characterize the underlying…
We consider the Navier-Stokes-Fourier-Poisson system driven by an inhomogeneous temperature distribution on the boundary of an exterior fluid domain. We impose the finite mass constraint, positive far field condition for the temperature as…
Recently, the discrete unified gas-kinetic scheme (DUGKS) [Z. L. Guo \emph{et al}., Phys. Rev. E ${\bf 88}$, 033305 (2013)] based on the Boltzmann equation is developed as a new multiscale kinetic method for isothermal flows. In this paper,…
This paper is devoted to the study of the Cauchy problem for the Boussinesq system with partial viscosity in dimension $N\geq3.$ First we prove a global existence result for data in Lorentz spaces satisfying a smallness condition which is…
The two-dimensional flow of viscous incompressible liquid in a square cavity with a free boundary and differentially heated vertical sides is considered in the present work. The influence of gravitational and thermocapillary convection on…
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…
The purpose of this article is to study the convergence of a low order finite element approximation for a natural convection problem. We prove that the discretization based on P1 polynomials for every variable (velocity, pressure and…
We study boundary value problems for bounded uniform domains in $\mathbb{R}^n$, $n\geq 2$, with non-Lipschitz (and possibly fractal) boundaries. We prove Poincar\'e inequalities with trace terms and uniform constants for uniform…
We consider two hydrodynamic model problems (one incompressible and one compressible) with three dimensional fluid flow on the torus and temperature-dependent viscosity and conductivity. The ambient heat for the fluid is transported by the…
We consider the d-dimensional Boussinesq system defined on a sufficiently smooth bounded domain, with homogeneous boundary conditions, and subject to external sources, assumed to cause instability. The initial conditions for both fluid and…