The regularity of the boundary of a multidimensional aggregation patch

A. Bertozzi, J. Garnett, T. Laurent, J. Verdera

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3 Citations (Scopus)

Abstract

© 2016 Society for Industrial and Applied Mathematics. We consider solutions to the aggregation equation with Newtonian potential where the initial data are the characteristic function of a domain with boundary of class C1+γ ,0 < γ < 1. Such initial data are known to yield a solution that, going forward in time, retains a patch-like structure with a constant time-dependent density inside an evolving region, which collapses on itself in a finite time, and which, going backward in time, converges in an L1 sense to a self-similar expanding ball solution. In this work, we prove C1+γ regularity of the domain's boundary on the time interval on which the solution exists as an L∞ patch, up to the collapse time going forward in time and for all finite times going backward in time.
Original languageEnglish
Pages (from-to)3789-3819
JournalSIAM Journal on Mathematical Analysis
Volume48
Issue number6
DOIs
Publication statusPublished - 1 Jan 2016

Keywords

  • Aggregation
  • C1+γ
  • High dimensional
  • Patch

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