Stochastic transport equation with singular drift. (English. French summary) Zbl 1537.35435
Summary: We prove existence, uniqueness and Sobolev regularity of weak solution of the Cauchy problem of the stochastic transport equation with drift in a large class of singular vector fields containing, in particular, the \(L^d\) class, the weak \(L^d\) class, as well as some vector fields that are not even in \(L_{\operatorname{loc}}^{2 + \varepsilon}\) for any \(\varepsilon > 0\).
MSC:
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 35A21 | Singularity in context of PDEs |
| 35Q49 | Transport equations |
Keywords:
stochastic transport equation; singular drift; stochastic differential equations; gradient estimatesReferences:
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