Related papers: Local existence of strong solutions to the stochas…

We address the local well-posedness for the stochastic Navier-Stokes system with multiplicative cylindrical noise in the whole space. More specifically, we prove that there exists a unique local strong solution to the system in…

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…

Considering the stochastic Navier-Stokes system in $\mathbb{R}^d$ forced by a multiplicative white noise, we establish the local existence and uniqueness of the strong solution when the initial data take values in the critical space…

We consider the stochastic Navier-Stokes equations with multiplicative noise with critical initial data. Assuming that the initial data $u_0$ belongs to the critical space $L^{3}$ almost surely, we construct a unique local-in-time…

In this paper we prove that the Navier-Stokes initial value problem (1) has a unique smooth local strong solution and if the following condition are satisfied (1) and is H\"older continuous about on, (2) The initial value

We address the global-in-time existence and pathwise uniqueness of solutions for the stochastic incompressible Navier-Stokes equations with a multiplicative noise on the three-dimensional torus. Under natural smallness conditions on the…

This paper treats the stationary Stokes problem in exterior domain of $\mathbb{R}^3$ with Navier slip boundary condition. The behavior at infinity of the data and the solution are determined by setting the problem in $L^p$-spaces, for $p>…

One proves the existence and uniqueness in $(L^p(\mathbb{R}^3))^3$, $\frac{3}{2}<p<2$, of a global mild solution to random vorticity equations associated to stochastic $3D$ Navier-Stokes equations with linear multiplicative Gaussian noise…

The aim of this article is to show a local-in-time existence of a strong solution to the generalized compressible Navier-Stokes equation for arbitrarily large initial data. The goal is reached by $L^p$-theory for linearized equations which…

In this paper, we show the existence and uniqueness of a strong solution to stochastic 3D tamed Navier-Stokes equations driven by multiplicative Levy noise with periodic boundary conditions. Then we establish the large deviation principles…

We study the Navier-Stokes equations on a smooth bounded domain $D\subset \mathbb R^d$ ($d=2$ or 3), under the effect of an additive fractional Brownian noise. We show local existence and uniqueness of a mild $L^p$-solution for $p>d$.

In this paper we are concerned with the 2D incompressible Navier-Stokes equations driven by space-time white noise. We establish existence of infinitely many global-in-time probabilistically strong and analytically weak solutions $u$ for…

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 consider the Navier-Stokes equations in vorticity form in $\mathbb{R}^2$ with a white noise forcing term of multiplicative type, whose spatial covariance is not regular enough to apply the It\^o calculus in $L^q$ spaces, $1<q<\infty$. We…

This work is devoted to the study of non-Newtonian fluids of grade three on two-dimensional and three-dimensional bounded domains, driven by a nonlinear multiplicative Wiener noise. More precisely, we establish the existence and uniqueness…

We study the existence and uniqueness of solutions of 2D Stochastic Navier-Stokes equation with space irregular jump noise for initial data in certain Sobolev spaces of negative order. Comparing with the Galerkin approximation method, the…

In this paper we prove the existence and uniqueness of a strong solution (in PDE sense) to the stochastic Navier-Stokes equations on the rotating 2-dimensional unit sphere perturbed by stable L\'evy noise. This strong solution turns out to…

We consider the Navier-Stokes equations in $\mathbb R^d$ ($d=2,3$) with a stochastic forcing term which is white noise in time and coloured in space; the spatial covariance of the noise is not too regular, so It\^o calculus cannot be…

We establish global-in-time existence and non-uniqueness of probabilistically strong solutions to the three dimensional Navier--Stokes system driven by space-time white noise. In this setting, solutions are expected to have space regularity…

We examine the so-called micropolar equations in three dimensional cylindrical domains under Navier boundary conditions. These equations form a generalization of the ordinary incompressible Navier-Stokes model, taking the structure of the…