Onsager's Conjecture for the Incompressible Euler Equations in the Hölog Spaces C^0,α_λ(Ω)

2019/12/23 by H. Beirão da Veiga, Jiaqi Yang, da Veiga, Hugo Beirão +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1912.10921

openalex publication_date 2019/12/23 · openalex created_date 2019/12/26 · openalex updated_date 2026/07/28

Abstract

In this note we extend a 2018 result of Bardos and Titi \citeBT to a new class of functional spaces C^0,α_λ(Ω). It is shown that weak solutions u satisfy the energy equality provided that u∈ L³((0,T);C^0,α_λ(Ω)) with α≥(1)/(3) and λ>0. The result is new for α= (1)/(3) . Actually, a quite stronger result holds. For convenience we start by a similar extension of a 1994 result of Constantin, E, and Titi, \citeCET, in the space periodic case. The proofs follow step by step those of the above authors. For the readers convenience, and completeness, proofs are presented in a quite complete form.

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