2014/09/18 by Hantaek Bae, Bae, Hantaek, James P. Kelliher +1 · 1 citation
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.1409.5169
openalex publication_date 2014/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1993, two proofs of the persistence of regularity of the boundary of a classical vortex patch for the 2D Euler equations were published, one by Chemin (announced in 1991) the other by Bertozzi and Constantin. Chemin, in fact, proved a more general result, extending it further in 1995 showing, roughly, that vorticity initially having discontinuities only in directions normal to a family of vector fields that together foliate the plane continue to be so characterized by the time-evolved vector fields. A different, four-page "elementary" proof of Chemin's 1993 result was published in 1994 by Ph. Serfati, who also gave a fuller characterization of the velocity gradient's regularity. We give a detailed version of Serfati's proof along with an extension of it to a family of vector fields that reproduces the 1995 result of Chemin.