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Register a new userStochastic transport equation with bounded and Dini continuous drift
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The results established by Flandoli, Gubinelli and Priola ({it Invent. Math.} {bf 180} (2010) 1--53) for stochastic transport equation with bounded and H{o}lder continuous drift are generalized to bounded and Dini continuous drift. The uniqueness of $L^infty$-solutions is established by the It^o--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.
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