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

A. V. Busuioc; D. Iftimie; M. C. Lopes Filho; H. J. Nussenzveig Lopes

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arXiv · 2002.09879

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

A. V. Busuioc·D. Iftimie·M. C. Lopes Filho·H. J. Nussenzveig Lopes

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Abstract

In this article we study the limit when $\alpha \to 0$ of solutions to the $\alpha$-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.

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A. V. Busuioc, D. Iftimie, M. C. Lopes Filho, H. J. Nussenzveig Lopes. 2020-02-23. The limit $\alpha \to 0$ of the $\alpha$-Euler equations in the half plane with no-slip boundary conditions and vortex sheet initial data. https://arxiv.org/abs/2002.09879

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