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\(W^{1,p}\)-solutions of the transport equation by stochastic perturbation. (English) Zbl 1434.60163
Summary: We consider the stochastic transport equation with a possibly unbounded Hölder continuous vector field. Well-posedness is proved, namely, we show existence, uniqueness and strong stability of \(W^{1,p}\)-weak solutions.
MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35F10 Initial value problems for linear first-order PDEs
35R60 PDEs with randomness, stochastic partial differential equations
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