A remark on global solutions to random 3D vorticity equations for small initial data
Probability
2018-03-06 v1
Abstract
In this paper, we prove that the solution constructed in \cite{BR16} satisfies the stochastic vorticity equations with the stochastic integration being understood in the sense of the integration of controlled rough path introduced in \cite{G04}. As a result, we obtain the existence and uniqueness of the global solutions to the stochastic vorticity equations in 3D case for the small initial data independent of time, which can be viewed as a stochastic version of the Kato-Fujita result (see \cite{KF62}).
Keywords
Cite
@article{arxiv.1803.01313,
title = {A remark on global solutions to random 3D vorticity equations for small initial data},
author = {Michael Röckner and Rongchan Zhu and Xiangchan Zhu},
journal= {arXiv preprint arXiv:1803.01313},
year = {2018}
}