Claude Bardos, Jasmine S. Linshiz, Edriss S. Titi
Published 2007-09-28, updated 2008-07-04Version 2
We present an alpha-regularization of the Birkhoff-Rott equation, induced by the two-dimensional Euler-alpha equations, for the vortex sheet dynamics. We show that initially smooth self-avoiding vortex sheet remains smooth for all times under the alpha-regularized dynamics, provided the initial density of vorticity is an integrable function over the curve with respect to the arc-length measure.
Comments: 7 pages, no figures, submitted to the proceedings of the Conference EE250, corrected typos, references added
Global regularity and convergence of a Birkhoff-Rott-alpha approximation of the dynamics of vortex sheets of the 2D Euler equations
Optimal Regularity for the 2D Euler Equations in the Yudovich class
Velocity blow-up in $C^1\cap H^2$ for the 2D Euler equations
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