Related papers: Global well-posedness for small data in a 3D tempe…
By applying Wiegner' method in \cite{Wiegner}, we first prove the large time decay estimate for the global solutions of a 2.5 dimensional Navier-Stokes system, which is a sort of singular perturbed 2-D Navier-Stokes system in three space…
In this paper, we will show that solutions of the three-dimensional non-resistive and non-diffusive MHD-Boussinesq system are globally regular if the initial data is axisymmetric and the swirl components of the velocity and the magnetic…
We establish existence of global-in-time weak solutions to the one dimensional, compressible Navier-Stokes system for a viscous and heat conducting ideal polytropic gas (pressure $p=K\theta/\tau$, internal energy $e=c_v \theta$), when the…
We investigate weak Serrin-type blowup criterion of the three-dimensional full compressible Navier-Stokes equations for the Cauchy problem, Dirichlet problem and Navier-slip boundary condition. It is shown that the strong or smooth solution…
In the present work, we investigate stochastic third grade fluids equations in a $d$-dimensional setting, for $d = 2, 3$. More precisely, on a bounded and simply connected domain $\mathcal{D}$ of $\mathbb{R}^d$, $d = 2,3$, with a…
We prove the strong ill-posedness in the sense of Hadamard of the two-dimensional Boussinesq equations in $W^{1, \infty}(\mathbb{R}^2)$ without boundary, extending to the case of systems the method that Shikh Khalil \& Elgindi…
In this article, we study the long time behavior of solutions of a variant of the Boussinesq system in which the equation for the velocity is parabolic while the equation for the temperature is hyperbolic. We prove that the system has a…
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…
We study solutions of the 2D Ginzburg-Landau equation -\Delta u+\frac{1}{\ve^2}u(|u|^2-1)=0 subject to "semi-stiff" boundary conditions: the Dirichlet condition for the modulus, |u|=1, and the homogeneous Neumann condition for the phase.…
Global well-posedness of the initial-boundary value problem for the stochastic Kuramoto-Sivashinsky equation in a bounded domain $D$ with a multiplicative noise is studied. It is shown that under suitable sufficient conditions, for any…
In this work we prove a global well-posedness result for a tridimensional rescaled Boussinesq system, with positive full viscosity and diffusivity parameters in the framework of critical Fourier-Besov spaces. This rescaled approach permits…
The Navier-Stokes equation driven by heat conduction is studied. As a prototype we consider Rayleigh-B\'enard convection, in the Boussinesq approximation. Under a large aspect ratio assumption, which is the case in Rayleigh-B\'enard…
In this work, we consider time-fractional Navier-Stokes equations (NSE) with the external forces involving finite delay. Equations are considered on a bounded domain in 3-D space having sufficiently smooth boundary. We transform the system…
We consider a class of bulk-surface coupled Cahn-Hilliard systems in a smooth, bounded domain $\Omega\subset\mathbb{R}^{d}$ $(d\in\{2,3\})$, where the trace value of the bulk phase variable is connected to the surface phase variable via a…
This paper is concerned with the initial-boundary value problem to 2D magnetohydrodynamics-Boussinesq system with the temperature-dependent viscosity, thermal diffusivity and electrical conductivity. First, we establish the global weak…
We study a Boussinesq system in a bounded domain with an outlet boundary portion where fluid can leave or re-enter. On this boundary part, we consider a do-nothing condition for the fluid flow, and a new artificial condition for the heat…
In this paper, we propose a novel uniform generalization bound on the time and inverse temperature for stochastic gradient Langevin dynamics (SGLD) in a non-convex setting. While previous works derive their generalization bounds by uniform…
We are concerned with the Cauchy problem of the full compressible Navier-Stokes equations satisfied by viscous and heat conducting fluids in $\mathbb{R}^n.$ We focus on the so-called critical Besov regularity framework. In this setting, it…
We consider a system of $d$ non-linear stochastic heat equations in spatial dimension $k \geq 1$, whose solution is an $\R^d$-valued random field $u= \{u(t\,,x),\, (t,x) \in \R_+ \times \R^k\}$. The $d$-dimensional driving noise is white in…
We establish the existence and uniqueness of local strong pathwise solutions to the stochastic Boussinesq equations with partial diffusion term forced by multiplicative noise on the torus in $\mathbb{R}^{d},d=2,3$. The solution is strong in…