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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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##### References:
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