Regularity criteria of the porous media equation in terms of one partial derivative or pressure field

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

We obtain new regularity criteria and smallness conditions for the global regularity of the N-dimensional supercritical porous media equation. In particular, it is shown that in order to obtain global regularity result, one only needs to bound a partial derivative in one direction or the pressure scalar field. Our smallness condition is also in terms of one direction, dropping conditions on (N -1) other directions completely, or the pressure scalar field. The proof relies on key observations concerning the incompressibility of the velocity vector field and the special identity derived from Darcy's law.

Original languageEnglish
Pages (from-to)461-476
Number of pages16
JournalCommunications in Mathematical Sciences
Volume13
Issue number2
DOIs
StatePublished - 2015

Keywords

  • Darcy's law
  • Porous media equation
  • Regularity criteria

Fingerprint Dive into the research topics of 'Regularity criteria of the porous media equation in terms of one partial derivative or pressure field'. Together they form a unique fingerprint.

  • Cite this