@article{523de83ff63e463cbb551558ff0c2de8,
title = "Stochastic transport equation with singular drift",
abstract = "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 Ld class, the weak Ld class, as well as some vector fields that are not even in L2loc+ε for any ε > 0.",
keywords = "Gradient estimates, Singular drift, Stochastic differential equations, Stochastic transport equation",
author = "Damir Kinzebulatov and Sem{\"e}nov, {Yuliy A.} and Renming Song",
note = "The research of D. K. is supported in part by a grant from the Natural Sciences and Engineering Research Council of Canada (RGPIN-2017-05567). The research of R. S. is supported in part by a grant from the Simons Foundation (#429343). Part of the research for this paper was done while the first-named author was supported by a grant of the Fonds de recherche du Qu{\'e}bec – Nature et technologies. Part of the research for this paper was done while the third-named author was visiting Jiangsu Normal University, where he was partially supported by a grant from the National Natural Science Foundation of China (11931004, Yingchao Xie).",
year = "2024",
month = feb,
doi = "10.1214/22-AIHP1353",
language = "English (US)",
volume = "60",
pages = "731--752",
journal = "Annales de l'institut Henri Poincare (B) Probability and Statistics",
issn = "0246-0203",
publisher = "Institute of Mathematical Statistics",
number = "1",
}