On a singular incompressible porous media equation

Susan Friedlander, Francisco Gancedo, Weiran Sun, Vlad Vicol

Research output: Contribution to journalArticlepeer-review


This paper considers a family of active scalar equations with transport velocities which are more singular by a derivative of order β than the active scalar. We prove that the equations with 0 < β ≤ 2 are Lipschitz ill-posed for regular initial data. On the contrary, when 0 < β < 1 we show local well-posedness for patch-type weak solutions.

Original languageEnglish (US)
Article number115602
JournalJournal of Mathematical Physics
Issue number11
StatePublished - Nov 27 2012

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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