Aggregation Equation and Collapse to Singular Measure

Taoufik Hmidi, Dong Li

Research output: Chapter in Book/Report/Conference proceedingChapter


We are concerned with the dynamics of onefold symmetric patches for the two-dimensional aggregation equation associated with the Newtonian potential. We reformulate a suitable graph model and prove a local well-posedness result in subcritical and critical spaces. The global existence is obtained only for small initial data using a weak damping property hidden in the velocity terms. This allows to analyze the concentration phenomenon of the aggregation patches near the blowup time. In particular, we prove that the patch collapses to a collection of disjoint segments, and we provide a description of the singular measure through a careful study of the asymptotic behavior of the graph.

Original languageEnglish (US)
Title of host publicationTutorials, Schools, and Workshops in the Mathematical Sciences
Number of pages27
StatePublished - 2022

Publication series

NameTutorials, Schools, and Workshops in the Mathematical Sciences
ISSN (Print)2522-0969
ISSN (Electronic)2522-0977


  • Aggregation equation
  • Asymptotic behavior
  • Concentration phenomenon

ASJC Scopus subject areas

  • General Mathematics
  • Physics and Astronomy (miscellaneous)


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