Related papers: Global well-posedness for small data in a 3D tempe…
We study the Navier-Stokes-Darcy-Boussinesq system that models the thermal convection of a fluid overlying a saturated porous medium in a general decomposed domain. In both two and three spatial dimensions, we first prove the existence of…
We consider a dynamic capillarity equation with stochastic forcing on a compact Riemannian manifold $(M,g)$. \begin{equation*}\tag{P} d \left(u_{\varepsilon,\delta}-\delta \Delta u_{\varepsilon,\delta}\right) +\operatorname{div}…
It is well known that the tropical climate model is an important model to describe the interaction of large scale flow fields and precipitation in the tropical atmosphere. In this paper, we address the issue of global well-posedness for 2D…
In this paper, we are concerned with the local and global existence for the stochastic Prandtl equation in two and three dimensions, which governs the velocity field inside the boundary layer that appears in the inviscid limit of the…
We consider the steady-state Boussinesq system in the whole three-dimensional space, with the action of external forces and the gravitational acceleration. First, for $3<p\leq +\infty$ we prove the existence of weak $L^p$-solutions.…
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…
This paper is concerned with an initial-boundary value problem of the two-dimensional inhomogeneous primitive equations with density-dependent viscosity. The global well-posedness of strong solutions is established, provided the initial…
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…
The nonhomogeneous Navier-Stokes equations with density-dependent viscosity is studied in three-dimensional (3D) exterior domains with nonslip or slip boundary conditions. We prove that the strong solutions exists globally in time provided…
We consider the stochastic heat equation with a multiplicative white noise forcing term under standard "intermitency conditions." The main finding of this paper is that, under mild regularity hypotheses, the a.s.-boundedness of the solution…
On a bounded three-dimensional smooth domain, we consider the generalized oscillon equation with Dirichlet boundary conditions, with time-dependent damping and time-dependent squared speed of propagation. Under structural assumptions on the…
We prove global well-posedness of the two-dimensional exterior Navier-Stokes equations for bounded initial data with a finite Dirichlet integral, subject to the non-slip boundary condition. As an application, we construct global solutions…
Natural convection is ubiquitous throughout the physical sciences and engineering, yet many of its important properties remain elusive. To study convection in a novel context, we derive and solve a quasilinear form of the Rayleigh-B\'enard…
We consider a gas in a horizontal slab, in which the top and bottom walls are kept at different temperatures. The system is described by the Boltzmann equation (BE) with Maxwellian boundary conditions specifying the wall temperatures. We…
We study the three-dimensional incompressible Navier-Stokes equations in a smooth bounded domain $\Omega$ with initial velocity $u_0$ square-integrable, divergence-free and tangent to $\partial \Omega$. We supplement the equations with the…
We consider the Navier--Stokes--Fourier system describing the motion of a compressible, viscous, and heat conducting fluid in a bounded domain with general non-homogeneous Dirichlet boundary conditions for the velocity and the absolute…
This paper considers the two-dimensional Cauchy problem of the full compressible Navier-Stokes equations with far-field vacuum in $\mathbb{R}^2$, where the viscosity and heat-conductivity coefficients depend on the absolute temperature…
In this paper, we consider the heat-conducting compressible self-gravitating fluids in time-dependent domains, which typically describe the motion of viscous gaseous stars. The flow is governed by the 3-D Navier-Stokes-Fourier-Poisson…
In this paper, we first prove the global existence of weak solutions to the d-dimensional incompressible inhomogeneous Navier-Stokes equations with initial data in critical Besov spaces, which satisfies a non-linear smallness condition. The…
The global well-posedness and stability of solutions to the three-dimensional compressible Euler equations with damping is a longstanding open problem. This problem was addressed in \cite{WY, STW} in the isentropic regime (i.e. $\gamma>1$)…