Euler Equations in Sobolev conormal spaces

2024/07/25 by Mustafa Sencer Aydın, Igor Kukavica, Aydın, Mustafa Sencer +1 · 1 citation
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2407.18149

openalex publication_date 2024/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We consider the three-dimensional incompressible Euler equations in Sobolev conormal spaces and establish local-in-time existence and uniqueness in the half-space or channel. The initial data is Lipschitz having four square-integrable conormal derivatives and two bounded conormal derivatives. We do not impose any integrability or differentiability assumption for the normal derivative.

Cited by

• A BKM-type criterion for the Euler equations

Related

• Inviscid limit on L^p-based Sobolev conormal spaces for the 3D Navier-Stokes equations with the Navier boundary conditions
• A BKM-type criterion for the Euler equations
• Conormal derivative problems for stationary Stokes system in Sobolev spaces
• Global well-posedness of helicoidal Euler equations
• The TURBO method for well-posedness of the incompressible Euler equations in Sobolev spaces in any domain