6 papers
Markov solutions for the 3D stochastic Navier--Stokes equations with state dependent noise
Arnaud Debussche, Cyril Odasso
We construct a Markov family of solutions for the 3D Navier-Stokes equation perturbed by a non degenerate noise. We improve the result of [DPD-NS3D] in two directions. We see that…
Spatial smoothness of the stationary solutions of the 3D Navier--Stokes equations
Cyril Odasso
We consider stationary solutions of the three dimensional Navier--Stokes equations (NS3D) with periodic boundary conditions and driven by an external force which might have a deter…
Exponential mixing for the 3D stochastic Navier--Stokes equations
Cyril Odasso
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 dege…
Exponential Mixing for Stochastic PDEs: The Non-Additive Case
Cyril Odasso
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 tim…
Ergodicity for the weakly damped stochastic non-linear Schrödinger equations
Arnaud Debussche, Cyril Odasso
We study a damped stochastic non-linear Schrödinger (NLS) equation driven by an additive noise. It is white in time and smooth in space. Using a coupling method, we establish conve…
Ergodicity for the stochastic Complex Ginzburg-Landau equations
Cyril Odasso
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 towa…