On a singular incompressible porous media equation

Susan Friedlander, Francisco Gancedo, Weiran Sun, Vlad Vicol

Research output: Contribution to journalArticle

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

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Porous Medium Equation
Scalar
scalars
Local Well-posedness
Weak Solution
Patch
Lipschitz
Derivative
Family

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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

On a singular incompressible porous media equation. / Friedlander, Susan; Gancedo, Francisco; Sun, Weiran; Vicol, Vlad.

In: Journal of Mathematical Physics, Vol. 53, No. 11, 115602, 27.11.2012.

Research output: Contribution to journalArticle

Friedlander, S, Gancedo, F, Sun, W & Vicol, V 2012, 'On a singular incompressible porous media equation', Journal of Mathematical Physics, vol. 53, no. 11, 115602. https://doi.org/10.1063/1.4725532
Friedlander, Susan ; Gancedo, Francisco ; Sun, Weiran ; Vicol, Vlad. / On a singular incompressible porous media equation. In: Journal of Mathematical Physics. 2012 ; Vol. 53, No. 11.
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