Well-posedness of the vector advection equations by stochastic perturbation

Abstract

A linear stochastic vector advection equation is considered. The equation may model a passive magnetic field in a random fluid. The driving velocity field is a integrable to a certain power and the noise is infinite dimensional. We prove that, thanks to the noise, the equation is well posed in a suitable sense, opposite to what may happen without noise.

arXiv commentWe made minor modifications