A REMARK ON GLOBAL SOLUTIONS TO RANDOM 3D VORTICITY EQUATIONS FOR SMALL INITIAL DATA
Röckner, Michael
Röckner
Michael
Zhu, Rongchan
Zhu
Rongchan
Zhu, Xiangchan
Zhu
Xiangchan
In this paper, we prove that the solution constructed in [2] satisfies the stochastic vorticity equations with the stochastic integration being understood in the sense of the integration of controlled rough path introduced in [x]. 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 [10]).
24
8
4021-4030
4021-4030
Amer Inst Mathematical Sciences-aims
2019