New dissipated energies for the thin fluid film equation

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The thin fluid film evolution ht = -(hnh xxx)x is known to conserve the fluid volume ∫ h dx and to dissipate the "energies" ∫ h1.5-n dx and ∫ hx2 dx. We extend this last result by showing the energy ∫ hphx2 dx is dissipated for some values of p < 0, when 1/2 < n < 3. For example when n = 1, the Hele-Shaw equation ht = -(hhxxx)x dissipates ∫ h -1/2hx2 dx.

Original languageEnglish (US)
Pages (from-to)613-634
Number of pages22
JournalCommunications on Pure and Applied Analysis
Issue number3
StatePublished - Sep 1 2005


  • Energy
  • Entropy
  • Film rupture
  • Lubrication approximation
  • Pinch-off
  • Thin fluid film

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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