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The results established by Flandoli, Gubinelli and Priola (Invent. Math. 180 (2010) 1– 53) for stochastic transport equation with bounded and Hölder continuous drift are generalized to bounded and Dini… Click to show full abstract
The results established by Flandoli, Gubinelli and Priola (Invent. Math. 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.
Journal Title: Journal of Differential Equations
Year Published: 2022
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