Energy-balance for the incompressible Euler equations with stochastic\n forcing

2020/10/29 by Shyam Sundar Ghoshal, Ghoshal, Shyam Sundar, Animesh Jana +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2010.15569

openalex publication_date 2020/10/29 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We establish energy-balance for weak solutions of the stochastically forced\nincompressible Euler equations, enjoying H "older regularity C^\α,\n\α>1/3. It is well known as the Onsager's conjecture for the\ndeterministic incompressible Euler equations, which describes the energy\nconservation of weak solutions having H "older regularity C^\α,\n\α>1/3. Additionally, we obtain energy-balance for the inhomogeneous\nincompressible Euler system driven by a cylindrical Wiener process.\n

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