Strong solution for stochastic transport equations with irregular drift: existence and non-existence
Analysis of PDEs
2017-11-15 v1
Abstract
We prove some existence, uniqueness and non-existence results of stochastic strong solutions for a class of stochastic transport equations with a -integrable (in time), bounded and -H\"{o}lder continuous (in space) drift coefficient. More precisely, we show that for a Sobolev differentiable initial condition, there exists a unique stochastic strong solution when , while for with spatial dimension higher than one, we can choose proper initial data and drift coefficients so that there is no stochastic strong solutions.
Cite
@article{arxiv.1711.05072,
title = {Strong solution for stochastic transport equations with irregular drift: existence and non-existence},
author = {Jinlong Wei and Jinqiao Duan and Hongjun Gao and Guangying Lv},
journal= {arXiv preprint arXiv:1711.05072},
year = {2017}
}