Noise Prevents Singularities in Linear Transport Equations
Probability
2013-03-19 v1 Analysis of PDEs
Abstract
A stochastic linear transport equation with multiplicative noise is considered and the question of no-blow-up is investigated. The drift is assumed only integrable to a certain power. Opposite to the deterministic case where smooth initial conditions may develop discontinuities, we prove that a certain Sobolev degree of regularity is maintained, which implies H\"older continuity of solutions. The proof is based on a careful analysis of the associated stochastic flow of characteristics.
Keywords
Cite
@article{arxiv.1205.5505,
title = {Noise Prevents Singularities in Linear Transport Equations},
author = {Ennio Fedrizzi and Franco Flandoli},
journal= {arXiv preprint arXiv:1205.5505},
year = {2013}
}