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

2010/07/23 by S. Attanasio, Stefano Attanasio, Attanasio, S. +3
Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.AP #math.PR

paper · pdf · doi:10.48550/arxiv.1007.4102

arxiv created 2010/07/23 · openalex publication_date 2010/07/23 · arxiv updated 2010/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A linear stochastic transport equation with non-regular coefficients is considered. Under the same assumption of the deterministic theory, all weak L^∞-solutions are renormalized. But then, if the noise is nondegenerate, uniqueness of weak L^∞-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.

Citations

• Uniqueness for a Stochastic Inviscid Dyadic Model

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