Now in its second edition, this book gives a systematic and self-contained presentation of
basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and …

The paper is concerned with the problem of regularization by noise of 3D Navier–Stokes
equations. As opposed to several attempts made with additive noise which remained …

This volume deals with the random perturbation of PDEs which lack well-posedness, mainly
because of their non-uniqueness, in some cases because of blow-up. The aim is to show …

We show the strong well-posedness of SDEs driven by general multiplicative Lévy noises
with Sobolev diffusion and jump coefficients and integrable drifts. Moreover, we also study …

We consider the ordinary differential equation (ODE) dxt= b (t, xt) d t+ dwt where w is a
continuous driving function and b is a time-dependent vector field which possibly is only a …

In the present paper we study fast-slow systems of coupled equations from fluid dynamics,
where the fast component is perturbed by additive noise. We prove that, under a suitable …

We prove local well-posedness in regular spaces and a Beale–Kato–Majda blow-up
criterion for a recently derived stochastic model of the 3D Euler fluid equation for …

In this paper we show the weak differentiability of the unique strong solution with respect to
the starting point x as well as Bismut–Elworthy–Li's derivative formula for the following …

In this paper linear stochastic transport and continuity equations with drift in critical L^p
spaces are considered. In this situation noise prevents shocks for the transport equation and …

Abstract Additive noise in Partial Differential equations, in particular those of fluid
mechanics, has relatively natural motivations. The aim of this work is showing that suitable …