小初值下三维随机涡度方程整体解的注记
A remark on global solutions to random 3D vorticity equations for small initial data
摘要：
本文证明了在\cite{BR16}中构造的解满足随机涡度方程，并将随机积分理解为\cite{G04}中引入的受控粗糙路径的积分。在小初值条件下，得到了三维随机涡度方程整体解的存在唯一性，这可以看作是Kato-Fujita结果（见\cite{KF62}）的随机版本.
英文摘要：
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}).
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