Related papers: Ergodicity for the weakly damped stochastic non-li…
This paper is devoted to proving the polynomial mixing for a weakly damped stochastic nonlinear Schr\"{o}dinger equation with additive noise on a 1D bounded domain. The noise is white in time and smooth in space. We consider both focusing…
This paper investigates exponential mixing of the invariant measure for randomly forced nonlinear Schr\"{o}dinger equation, with damping and random noise localized in space. Our study emphasizes the crucial role of exponential asymptotic…
We study a stochastic complex Ginzburg--Landau (CGL) equation driven by a smooth noise in space and we establish exponential convergence of the Markovian transition semi-group toward a unique invariant probability measure. Since Doob…
In this paper, we investigate the convergence order in probability of a novel ergodic numerical scheme for damped stochastic nonlinear Schr\"{o}dinger equation with an additive noise. Theoretical analysis shows that our scheme is of order…
In this paper, we consider the well-posedness of the weakly damped stochastic nonlinear Schr\"odinger(NLS) equation driven by multiplicative noise. First, we show the global existence of the unique solution for the damped stochastic NLS…
We study the long time statistics of a class of semi--linear wave equations modeling the motions of a particle suspended in continuous media while being subjected to random perturbations via an additive Gaussian noise. By comparison with…
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…
In this paper, we investigate the damped stochastic nonlinear Schr\"odinger(NLS) equation with multiplicative noise and its splitting-based approximation. When the damped effect is large enough, we prove that the solutions of the damped…
In order to inherit numerically the ergodicity of the damped stochastic nonlinear Schr\"odinger equation with additive noise, we propose a fully discrete scheme, whose spatial direction is based on spectral Galerkin method and temporal…
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…
Several theories for weakly damped free-surface flows have been formulated. In this paper we use the linear approximation to the Navier-Stokes equations to derive a new set of equations for potential flow which include dissipation due to…
We study the nonlinear Schr\"odinger equation with linear damping, i.e. a zero order dissipation, and additive noise. Working in $R^d$ with d = 2 or d = 3, we prove the uniqueness of the invariant measure when the damping coefficient is…
The paper is devoted to studying the stochastic nonlinear wave (NLW) equation in a bounded domain D $\subset$ R3. We show that the Markov process associated with the flow of solution has a unique stationary measure $\mu$, and the law of any…
We prove the exponential convergence to a unique invariant measure for locally damped nonlinear Schr\"odinger equations, perturbed by bounded noise acting on only two Fourier modes. To tackle the lack of smoothing effect, we introduce…
Recently, a number of authors have investigated the conditions under which a stochastic perturbation acting on an infinite dimensional dynamical system, e.g. a partial differential equation, makes the system ergodic and mixing. In…
We consider a finite dimensional approximation of the stochastic nonlinear Schr\"odinger equation driven by multiplicative noise, which is derived by applying a symplectic method to the original equation in spatial direction. Both the…
We establish a general criterion which ensures exponential mixing of parabolic Stochastic Partial Differential Equations (SPDE) driven by a non additive noise which is white in time and smooth in space. We apply this criterion on two…
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,…
In this paper, we investigate the convergence in probability of a stochastic symplectic scheme for stochastic nonlinear Schr\"{o}dinger equation with quadratic potential and an additive noise. Theoretical analysis shows that our symplectic…
We study the long-time mixing behavior of the stochastic nonlinear Schr\"odinger equation in $\mathbb{R}^d$, $d\le 3$. It is well known that, under a sufficiently strong damping force, the system admits unique ergodicity, although the rate…