Well-posedness of the stochastic transport equation with unbounded drift

2015/07/16 by Mollinedo, David A. C., Olivera, Christian
#35F10 #35R60 #60H15 #60H30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1507.04559

Abstract

The Cauchy problem for a multidimensional linear transport equation with unbounded drift is investigated. Provided the drift is Holder continuous , existence, uniqueness and strong stability of solutions are obtained. The proofs are based on a careful analysis of the associated stochastic flow of characteristics and techniques of stochastic analysis.

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