The Regularity of the Boundary of a Multidimensional Aggregation Patch
Skip to main content
eScholarship
Open Access Publications from the University of California

The Regularity of the Boundary of a Multidimensional Aggregation Patch

  • Author(s): Bertozzi, A
  • Garnett, J
  • Laurent, T
  • Verdera, J
  • et al.
Abstract

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.

Many UC-authored scholarly publications are freely available on this site because of the UC Academic Senate's Open Access Policy. Let us know how this access is important for you.

Main Content
Current View