Related papers: Ergodicity for stochastic equation of Navier--Stok…

Stochastic Navier--Stokes equations in a thin three-dimensional domain are considered, driven by additive noise. The convergence of martingale solution of the stochastic Navier--Stokes equations in a thin three-dimensional domain to the…

In this paper we study a system of stochastic differential equations with dissipative nonlinearity which arise in certain neurobiology models. Besides proving existence, uniqueness and continuous dependence on the initial datum, we shall be…

The two dimensional Navier-Stokes equation in a perforated domain with a dynamical slip boundary condition is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior of the domain and another stochastic…

This paper is dedicated to the construction of a pseudo-norm, for which small shock profiles of the barotropic Navier-Stokes equation have a contraction property. This contraction property holds in the class of any large 1D weak solutions…

Regularization by noise for certain classes of fluid dynamic equations, a theme dear to Giuseppe Da Prato (see G. Da Prato and A. Debussche, Ergodicity for the 3D stochastic Navier-Stokes equations, J. Math. Pures Appl., 2003), is reviewed…

In this paper we first prove the existence and uniqueness of the solution to the stochastic Navier--Stokes equations on the rotating 2-dimensional sphere. Then we show the existence of an asymptotically compact random dynamical system…

The stability problem for the 2D Navier-Stokes equations with dissipation in only one direction on $\mathbb R^2$ is not fully understood. This dissipation is in the intermediate regime between the fully dissipative Navier-Stokes and the…

We survey the recent advance in the rigorous qualitative theory of the 2d stochastic Navier-Stokes system that are relevant to the description of turbulence in two-dimensional fluids. After discussing briefly the initial-boundary value…

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 article, we consider a novel version of three-dimensional (3D) globally modified Navier-Stokes (GMNS) system introduced by [Caraballo et. al., Adv. Nonlinear Stud. (2006), 6:411-436], which is very significant from the perspective…

We study the motion of a particle in a random time-dependent vector field defined by the 2D Navier-Stokes system with a noise. Under suitable non-degeneracy hypotheses we prove that the empirical measures of the trajectories of the pair…

We discrete the ergodic semilinear stochastic partial differential equations in space dimension $d \leq 3$ with additive noise, spatially by a spectral Galerkin method and temporally by an exponential Euler scheme. It is shown that both the…

We consider the 2d $\beta$-plane stochastic Navier-Stokes equations in a periodic channel. We prove the well-posedness and existence of the stationary measure, as well as certain regularity estimates concerning the support of the stationary…

We consider the Kolmogorov operator $K$ associated to a stochastic Navier-Stokes equation driven by space-time white noise on the two-dimensional torus with periodic boundary conditions and a rotating reference frame, introducing fictitious…

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 prove that there exists a weak solution to a system governing an unsteady flow of a viscoelastic fluid in three dimensions, for arbitrarily large time interval and data. The fluid is described by the incompressible Navier-Stokes…

We study the Navier-Stokes equations governing the motion of isentropic compressible fluid in three dimensions driven by a multiplicative stochastic forcing. In particular, we consider a stochastic perturbation of the system as a function…

This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with…

A stochastic variational inequality is proposed to model an elasto-plastic oscillator excited by a filtered white noise. We prove the ergodic properties of the process and characterize the corresponding invariant measure. This extends…

We calculate in this work the Navier-Stokes transport coefficients from the Boltzmann equation for $d$-dimensional inelastic Maxwell models. By granular gas we mean here a low density system of identical spheres that lose a fraction of…