On a singular incompressible porous media equation

Susan Friedlander, Francisco Gancedo, Weiran Sun, Vlad Vicol

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Abstract

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
Volume53
Issue number11
DOIs
StatePublished - Nov 27 2012

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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    Friedlander, S., Gancedo, F., Sun, W., & Vicol, V. (2012). On a singular incompressible porous media equation. Journal of Mathematical Physics, 53(11), [115602]. https://doi.org/10.1063/1.4725532