2022/10/06 by Andréa Agazzi, Agazzi, Andrea, Jonathan C. Mattingly +3
Economics, Econometrics and Finance · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2210.02958
openalex publication_date 2022/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we give sufficient conditions for random splitting systems to have a positive top Lyapunov exponent. We verify these conditions for random splittings of two fluid models: the conservative Lorenz-96 equations and Galerkin approximations of the 2D Euler equations on the torus. In doing so, we highlight particular structures in these equations such as shearing. Since a positive top Lyapunov exponent is an indicator of chaos which in turn is a feature of turbulence, our results show these randomly split fluid models have important characteristics of turbulent flow.