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Article Contents

# A remark on global solutions to random 3D vorticity equations for small initial data

• * Corresponding author

Supported in part by NSFC (11671035, 11771037). Financial support by the DFG through the CRC 1283"Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics and their applications" is acknowledged

• 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 [8]. 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]).

Mathematics Subject Classification: 60H15, 82C28.

 Citation:

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