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Large deviations of invariant measure for the 3D stochastic hyperdissipative Navier-Stokes equations

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arxiv 2307.04271 v1 pith:5LYRWGCR submitted 2023-07-09 math.AP math.PR

Zhaoyang Qiu , Hui Liu , Chengfeng Sun This is my paper
classification math.APmath.PR
keywords deviationslargeinvariantmeasureuniformequationsergodicityexponential
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In this paper, we consider the large deviations of invariant measure for the 3D stochastic hyperdissipative Navier-Stokes equations driven by additive noise. The unique ergodicity of invariant measure as a preliminary result is proved using a deterministic argument by the exponential moment and exponential stability estimates. Then, the uniform large deviations is established by the uniform contraction principle. Finally, using the unique ergodicity and the uniform large deviations results, we prove the large deviations of invariant measure by verifying the Freidlin-Wentzell large deviations upper and lower bounds.

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