Related papers: Three-Dimensional stochastic Navier-Stokes equatio…
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.…
We prove that every Markov solution to the three dimensional Navier-Stokes equation with periodic boundary conditions driven by additive Gaussian noise is uniquely ergodic. The convergence to the (unique) invariant measure is exponentially…
We study the long-time behavior of solutions to a stochastically driven Navier-Stokes system describing the motion of a compressible viscous fluid driven by a temporal multiplicative white noise perturbation. The existence of stationary…
We consider the control problem of the stochastic Navier-Stokes equations in multidimensional domains introduced in \cite{ocpc} restricted to noise terms defined by Q-Wiener processes. Using a stochastic maximum principle, we derive a…
The main purpose of this paper is to show that Markov solutions to the 3D Navier--Stokes equations driven by Gaussian noise have the strong Feller property up to the critical topology given by the domain of the Stokes operator to the power…
We are concerned with the three dimensional navier-stokes equations driven by a general multiplicative noise. For every divergence free and mean free initial condition in L2, we establish existence of infinitely many global-in-time…
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…
The existence of suitable weak solutions of 3D Navier-Stokes equations, driven by a random body force, is proved. These solutions satisfy a local balance of energy. Moreover it is proved also the existence of a statistically stationary…
We consider randomly forced 2D Navier-Stokes equations in a bounded domain with smooth boundary. It is assumed that the random perturba- tion is non-degenerate, and its law is periodic in time and has a support localised with respect 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…
In this paper we discuss backward stochastic differential equations with Markov chain noise, having continuous drivers. We obtain the existence of a solution which is possibly not unique. Moreover, we show there is a minimal solution for…
We study the three dimensional stochastic Zakharov system in the energy space, where the Schr\"odinger equation is driven by linear multiplicative noise and the wave equation is driven by additive noise. We prove the well-posedness of the…
This paper is concerned with stochastic incompressible Navier-Stokes equations with multiplicative noise in two dimensions with respect to periodic boundary conditions. Based on the Helmholtz decomposition of the multiplicative noise,…
We prove that the any Markov solution to the 3D stochastic Navier-Stokes equations driven by a mildly degenerate noise (i.e.all but finitely many Fourier modes are forced) is uniquely ergodic. This follows by proving strong Feller…
We investigate the Markov property and the continuity with respect to the initial conditions (strong Feller property) for the solutions to the Navier-Stokes equations forced by an additive noise. First, we prove, by means of an abstract…
We study (backward) stochastic differential equations with noise coming from a finite state Markov chain. We show that, for the solutions of these equations to be `Markovian', in the sense that they are deterministic functions of the state…
We propose and study a temporal, and spatio-temporal discretisation of the 2D stochastic Navier--Stokes equations in bounded domains supplemented with no-slip boundary conditions. Considering additive noise, we base its construction on the…
We address a slow-fast system of coupled three dimensional Navier--Stokes equations where the fast component is perturbed by an additive Brownian noise. By means of the rough path theory, we establish the convergence in law of the slow…
This work proposes an efficient, linear, and fully decoupled pressure-correction scheme for the 2D stochastic Navier-Stokes equations with multiplicative noise and Dirichlet boundary condition. Leveraging the auxiliary variable approach,…
We study the Navier-Stokes equations with an extra eddy viscosity term in the whole space in three dimensions. We introduce a suitable regularized system for which we prove the existence of a regular solution defined for all time. We prove…