Well-posedness of the stochastic transport equation with unbounded drift
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driftstochasticanalysisequationtransportunboundedassociatedcareful
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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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