Related papers: Global L_2-solutions of stochastic Navier-Stokes e…

We consider the global existence and large-time asymptotic behavior of strong solutions to the Cauchy problem of the three-dimensional nonhomogeneous incompressible Navier-Stokes equations with density-dependent viscosity and vacuum. We…

Consider the Cauchy problem of incompressible Navier-Stokes equations in $\mathbb{R}^3$ with uniformly locally square integrable initial data. If the square integral of the initial datum on a ball vanishes as the ball goes to infinity, the…

In this paper we prove the almost sure existence of global weak solution to the 3D incompressible Navier-Stokes Equation for a set of large data in $\dot{H}^{-\alpha}(\mathbb{R}^{3})$ or $\dot{H}^{-\alpha}(\mathbb{T}^{3})$ with…

In this paper, we solve Lions' open problem: {\it the uniqueness of weak solutions for the 2-D inhomogeneous Navier-Stokes equations (INS)}. We first prove the global existence of weak solutions to 2-D (INS) with bounded initial density and…

We study the theory of local and global strong solution for the stochastic tamed Navier--Stokes equations with multiplicative Wiener and L\'evy jump noise in the whole space $\R^3$. More specifically, we first prove the existence of a…

In this paper, we consider the three-dimensional inhomogeneous Navier-Stokes equations with density-dependent viscosity in presence of vacuum over bounded domains. Global-in-time unique strong solution is proved to exist when $\|\nabla…

We are dealing with the Navier-Stokes equation in a bounded regular domain $D$ of $\mathbb{R}^2$, perturbed by an additive Gaussian noise $\partial w^{Q_\delta}/\partial t$, which is white in time and colored in space. We assume that the…

We address the global existence of solutions to the stochastic Navier-Stokes equations with multiplicative noise and with initial data in $H^{1/2}(\mathbb{T}^{3})$. We prove that the solution exists globally in time with probability…

We study 2D Navier-Stokes equations with a constraint on $L^2$ energy of the solution. We prove the existence and uniqueness of a global solution for the constrained Navier-Stokes equation on $\R^2$ and $\T$, by a fixed point argument. We…

Consider the unforced incompressible homogeneous Navier-Stokes equations on the $d$-torus $\mathbb{T}^d$ where $d\geq 4$ is the space dimension. It is shown that there exist nontrivial steady-state weak solutions $u\in L^{2}(\mathbb{T}^d)$.…

In this paper, we investigate Cauchy problem of the two-dimensional full Maxwell-Navier-Stokes system, and prove the global-in-time existence and uniqueness of solution in the borderline space which is very close to $L^2$-energy space by…

We consider the steady-state Navier-Stokes equation in the whole space $\mathbb{R}^3$ driven by a forcing function $f$. The class of source functions $f$ under consideration yield the existence of at least one solution with finite Dirichlet…

We show that any solution of the two-dimensional Navier-Stokes equation whose vorticity distribution is uniformly bounded in $L^1(R^2)$ for positive times is entirely determined by the trace of the vorticity at $t = 0$, which is a finite…

In this paper, we consider the Cauchy problem for the three-dimensional barotropic compressible Navier-Stokes equations with density-dependent viscosities. By considering the system as an elliptic-dominated structure and defining suitable…

This paper is devoted to the global solvability of the Navier-Stokes system with fractional Laplacian $(-\Delta)^{\alpha}$ in $\mathbb{R}^{n}$ for $n\geq2$, where the convective term has the form $(|u|^{m-1}u)\cdot\nabla u$ for $m\geq1$. By…

This paper is concerned with the weak solution theory for the MHD system with large $L^3$-initial data. Due to the fact that the natural boundary condition on the magnetic field $H$ is the slip boundary condition, the Leray-Schauder…

In this paper, we prove the global existence, uniqueness and the continuity in $L^2$ of the incompressible Navier-Stokes equations with damping $f(|u|)u$, where $f$ is an increasing, convex and differentiable function on $\mathbb{R}^+$,…

Martingale solutions of stochastic Navier-Stokes equations in 2D and 3D possibly unbounded domains, driven by the L\'evy noise consisting of the compensated time homogeneous Poisson random measure and the Wiener process are considered.…

This article is devoted to the well-posedness of the stochastic compressible Navier Stokes equations. We establish the global existence of an appropriate class of weak solutions emanating from large inital data, set within a bounded domain.…

Here we investigate the Cauchy problem for the inhomogeneous Navier-Stokes equations in the whole $n$-dimensional space. Under some smallness assumption on the data, we show the existence of global-in-time unique solutions in a critical…