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

2023/03/09 by Wen Huang, Jianhua Zhang, Huang, Wen +1
Computer Science · Economics, Econometrics and Finance · Engineering · #37A50 #37H05 #60H10 #Advanced Mathematical Modeling in Engineering #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2303.05027

openalex publication_date 2023/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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