Strong solutions for two-phase free boundary problems for a class of non-Newtonian fluids

Matthias Georg Hieber, Hirokazu Saito

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Consider the two-phase free boundary problem subject to surface tension and gravitational forces for a class of non-Newtonian fluids with stress tensors Tn of the form (Formula presented.) for (Formula presented.), respectively, where the viscosity functions (Formula presented.) satisfy (Formula presented.) and (Formula presented.) for (Formula presented.). It is shown that for given (Formula presented.) this problem admits a unique strong solution on (0,T) provided the initial data are sufficiently small in their natural norms.

Original languageEnglish
Pages (from-to)1-24
Number of pages24
JournalJournal of Evolution Equations
DOIs
Publication statusAccepted/In press - 2016 Sep 19
Externally publishedYes

Keywords

  • non-Newtonian fluids
  • strong solutions
  • surface tension
  • Two-phase free boundary problems

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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