Global regularity and convergence of a Birkhoff-Rott-α approximation of the dynamics of vortex sheets of the 2D Euler equations

Jasmine S. Linshiz (1) , Claude Bardos (2) , Edriss S. Titi (3)

1 Department of Computer Science and Applied Mathematics [Rehovot]
2 LJLL - Laboratoire Jacques-Louis Lions
3 DMDMAE - Department of Mathematics and Department of Mechanical and Aerospace Engineering

We present an alpha regularization of the Birkhoff-Rott equation, induced by the two-dimensional Euler equation, for the vortex sheet dynamics. We show the convergence of the solutions of Euler alpha equations to a weak solution of the Euler equations

Domaines: Analyse numérique [cs.NA]

Jasmine S. Linshiz, Claude Bardos, Edriss S. Titi. Global regularity and convergence of a Birkhoff-Rott-α approximation of the dynamics of vortex sheets of the 2D Euler equations. 2009. ⟨hal-00392118⟩