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arXiv · 1611.05300

Weak solutions for the $α$-Euler equations and convergence to Euler

Adriana Valentina Busuioc·Dragoş Iftimie
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Abstract

We consider the limit $α\to0$ for the $α$-Euler equations in a two-dimensional bounded domain with Dirichlet boundary conditions. Assuming that the vorticity is bounded in $L^p$, we prove the existence of a global solution and we show the convergence towards a solution of the incompressible Euler equation with $L^p$ vorticity. The domain can be multiply-connected. We also discuss the case of the second grade fluid when both $α$ and $ν$ go to 0.

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Adriana Valentina Busuioc, Dragoş Iftimie. 2016-11-16. Weak solutions for the $α$-Euler equations and convergence to Euler. https://doi.org/10.1088/1361-6544%2Faa8982

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