On the energy and helicity conservation of the incompressible Euler equations

2023/07/17 by Yanqing Wang, Wei Wei, Wang, Yanqing +5 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2307.08322

openalex publication_date 2023/07/17 · openalex created_date 2023/07/19 · openalex updated_date 2026/07/28

Abstract

In this paper, we are concerned with the minimal regularity of weak solutions implying the law of balance for both energy and helicity in the incompressible Euler equations. In the spirit of recent works due to Berselli [5] and Berselli-Georgiadis [6], it is shown that the energy of weak solutions is invariant if v∈ L^p(0,T;B^\frac1p_{(2p)/(p-1),c(ℕ)} ) with 1

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