Uniform time of existence for the alpha Euler equations

2015/09/04 by A. V. Busuioc, Adriana Valentina Busuioc, Dragoş Iftimie +9 · 1 citation
Computer Science · Mathematics · #35Q30 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #math.AP #msc:35Q30

paper · pdf · doi:10.48550/arxiv.1509.01625

arxiv created 2015/09/04 · openalex publication_date 2015/09/04 · arxiv updated 2015/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the α-Euler equations on a bounded three-dimensional domain with frictionless Navier boundary conditions. Our main result is the existence of a strong solution on a positive time interval, uniform in α, for α sufficiently small. Combined with the convergence result in a previous article by the same authors, this implies convergence of solutions of the α-Euler equations to solutions of the incompressible Euler equations when α→ 0. In addition, we obtain a new result on local existence of strong solutions for the incompressible Euler equations on bounded three-dimensional domains. The proofs are based on new \it a priori estimates in conormal spaces.

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