2007/09/30 by Claude Bardos, Jasmine S. Linshiz, Edriss S. Titi
Earth and Planetary Sciences · Engineering · Mathematics · #Euler equations #Euler's formula #Fluid Dynamics and Turbulent Flows #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Mechanics #Navier-Stokes equation solutions #Oceanographic and Atmospheric Processes #Physics #Regularization (linguistics) #Vortex #Vortex sheet #Vorticity #math.AP #msc:35Q35 #msc:76B03 #msc:76B47
paper · pdf · doi:10.1016/j.physd.2008.01.003
7 pages, no figures, submitted to the proceedings of the Conference EE250, corrected typos, references added
openalex publication_date 2008/03/06 · arxiv created 2008/07/04 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.