arXiv subjects

A. V. Busuioc

Publications and source records attributed to A. V. Busuioc.

2 recordsLinked to original sources

arXiv2020

The limit $α\to 0$ of the $α$-Euler equations in the half plane with no-slip boundary conditions and vortex sheet initial data

In this article we study the limit when $α\to 0$ of solutions to the $α$-Euler system in the half-plane, with no-slip boundary conditions, to weak solutions of the 2D incompressible Euler equations with non-negative initial vorticity in the space of bounded Radon measures in $H^{-1}$. This result extends the analysis done in arXiv:1611.05300 and arXiv:1403.5682. It requires a substantially distinct approach, analogous to that used for Delort's Theorem, and a new detailed investigation of the relation between (no-slip) filtered velocity and potential vorticity in the half-plane.

math.AP↗

arXiv2015

Uniform time of existence for the alpha Euler equations

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 $α\to 0$. 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.

math.AP↗