We prove that the subquartic wave equation on the three dimensional ball Θ, with Dirichlet
boundary conditions admits global strong solutions for a large set of random supercritical …

We analyze the decay and instant regularization properties of the evolution semigroups
generated by two-dimensional drift-diffusion equations in which the scalar is advected by a …

In [12], we constructed and proved the invariance of a Gibbs measure associated to the sub-
cubic, focusing or defocusing Nonlinear Schrödinger equation (NLS) on the disc of the plane …

We prove that the Schrödinger equation is approximately controllable in Sobolev spaces Hs,
s> 0, generically with respect to the potential. We give two applications of this result. First, in …

We consider the vorticity form of the 2D Euler equations which is perturbed by a suitable
transport type noise and has white noise initial condition. It is shown that stationary solutions …

We study Gibbs measures invariant under the flow of the NLS on the unit disc of $\R^ 2$. For
that purpose, we construct the dynamics on a phase space of limited Sobolev regularity and …

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 …

We study the long time behavior of the subcritical (subcubic) defocussing nonlinear wave
equation on the three dimensional ball, for random data of low regularity. We prove that for a …

We study the limiting behavior of the two-dimensional singular stochastic stochastic cubic
nonlinear complex Ginzburg-Landau with Gibbs measure initial data. We show that in 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 …