相关论文: Ergodicity and mixing for stochastic partial diffe…

We consider the Navier-Stokes equation on a two dimensional torus with a random force which is white noise in time, and excites only a finite number of modes. The number of excited modes depends on the viscosity $\nu$, and grows like…

In the first part of the note we analyze the long time behaviour of a two dimensional stochastic Navier--Stokes equations system on a torus with a degenerate, one dimensional noise. In particular, for some initial data and noises we…

The stochastic 2D Navier-Stokes equations on the torus driven by degenerate noise are studied. We characterize the smallest closed invariant subspace for this model and show that the dynamics restricted to that subspace is ergodic. In…

We prove ergodicity of the finite dimensional approximations of the three dimensional Navier-Stokes equations, driven by a random force. The forcing noise acts only on a few modes and some algebraic conditions on the forced modes are found…

The ergodic properties of the randomly forced Navier-Stokes system have been extensively studied in the literature during the last two decades. The problem has always been considered in bounded domains, in order to have, for example,…

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 2D stochastic Navier-Stokes equations driven by noise that has the regularity of space-time white noise but doesn't exactly coincide with it. We show that, provided that the intensity of the noise is sufficiently weak at…

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…

Asymptotic behavior of the three-dimensional stochastic Navier-Stokes equations with Markov switching in additive noises is studied for incompressible fluid flow in a bounded domain in the three-dimensional space. To study such a system, we…

The objective of this note is to present the results from the two recent papers. We study the Navier--Stokes equation on the two--dimensional torus when forced by a finite dimensional white Gaussian noise. We give conditions under which…

We study the global-in-time dynamics for a stochastic semilinear wave equation with cubic defocusing nonlinearity and additive noise, posed on the $2$-dimensional torus. The noise is taken to be slightly more regular than space-time white…

In this paper, we establish ergodic and mixing properties of stochastic 2D Navier-Stokes equations driven by a highly degenerate multiplicative Gaussian noise. The noise could appear in as few as four directions and the intensity of the…

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 consider an electrodiffusion model that describes the intricate interplay of multiple ionic species with a two-dimensional, incompressible, viscous fluid subjected to stochastic additive noise. This system involves nonlocal nonlinear…

We prove existence of infinitely many stationary solutions as well as ergodic stationary solutions for the stochastic Navier-Stokes equations on $\mathbb{T}^2$ \begin{align*} \dif u+\div(u\otimes u)\dif t+\nabla p\dif t&=\Delta u\dif t +…

We study the Navier-Stokes equations in dimension 3 (NS3D) driven by a noise which is white in time. We establish that if the noise is at same time sufficiently smooth and non degenerate in space, then the weak solutions converge…

In this paper, we establish the ergodicity for stochastic 2D Navier-Stokes equations driven by a highly degenerate pure jump L\'evy noise. The noise could appear in as few as four directions. This gives an affirmative anwser to a…

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 establish general quantitative conditions for stochastic evolution equations with locally monotone drift and degenerate additive Wiener noise in variational formulation resulting in the existence of a unique invariant probability measure…

This paper is concerned with the ergodicity for stochastic 2D fractional magneto-hydrodynamic equations on the two-dimensional torus driven by a highly degenerate pure jump L\'{e}vy noise. We focus on the challenging case where the noise…