Renormalized solutions for stochastic transport equations and the regularization by bilinear multiplicative noise

Abstract

A linear stochastic transport equation with non-regular coefficients is considered. Under the same assumption of the deterministic theory, all weak $L^{\infty }$-solutions are renormalized. But then, if the noise is nondegenerate, uniqueness of weak $L^{\infty }$-solutions does not require essential new assumptions, opposite to the deterministic case where for instance the divergence of the drift is asked to be bounded. The proof gives a new explanation why bilinear multiplicative noise may have a regularizing effect.

References in corpus (1)

• Uniqueness for a Stochastic Inviscid Dyadic Model

Cited by in corpus (1)

• Random perturbations of nonlinear parabolic systems