Uniform time of existence for the alpha Euler equations

Abstract

We consider the $\alpha$-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 $\alpha$, for $\alpha$ sufficiently small. Combined with the convergence result in a previous article by the same authors, this implies convergence of solutions of the $\alpha$-Euler equations to solutions of the incompressible Euler equations when $\alpha \to 0$. 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.

References in corpus (2)

• On the convergence rate of the Euler-$\alpha$, an inviscid second-grade complex fluid, model to the Euler equations
• Convergence of the 2D Euler-$\alpha$ to Euler equations in the Dirichlet case: indifference to boundary layers