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Full-horseshoes for the Galerkin truncations of 2D Navier-Stokes equation with degenerate stochastic forcing

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arxiv 2303.05027 v3 pith:7WFZE2AG submitted 2023-03-09 math.DS math-phmath.MP

Wen Huang , Jianhua Zhang This is my paper · ORCID
classification math.DSmath-phmath.MP
keywords forcingfull-horseshoesstochasticdegenerateequationgalerkinkindnavier-stokes
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In this paper, we mainly study the turbulence of Galerkin truncations of 2D Navier-Stokes equation under degenerate stochastic forcing and large-scale. We use a kind of chaotic structure named full-horseshoes to describe it. It is proved that if the stochastic forcing satisfies some kind of hypoelliptic condition, then the system has full-horseshoes.

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  1. Non uniform expansion and additive noise imply random horseshoe

    math.DS 2025-01 reject novelty 7.0 of 10

    Non-uniformly expanding maps with additive noise and a fully-positive-Lyapunov stationary measure are asserted to have dense random horseshoes, a random version of Smale's horseshoe.

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