Stochastic transport equation with bounded and Dini continuous drift

2021/05/18 by Wei, Jinlong, Lv, Guangying, Wang, Wei
#60H15 (35A01 35L02) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2105.08465

Abstract

The results established by Flandoli, Gubinelli and Priola (\it Invent. Math. \bf 180 (2010) 1--53) for stochastic transport equation with bounded and Hölder continuous drift are generalized to bounded and Dini continuous drift. The uniqueness of L^∞-solutions is established by the Itô--Tanaka trick partially solving the uniqueness problem, which is still open, for stochastic transport equation with only bounded measurable drift. Moreover the existence and uniqueness of stochastic diffeomorphisms flows for a stochastic differential equation with bounded and Dini continuous drift is obtained.

Related

• Stochastic flows for Hölder drifts and transport/continuity equations with noise
• Well-posedness of the stochastic transport equation with unbounded drift
• Remarks on the stochastic transport equation with Hölder drift
• Flow of diffeomorphisms for SDEs with unbounded Hölder continuous drift
• Strong solution for stochastic transport equations with irregular drift: existence and non-existence