The nonlinear stokes problem with general potentials having superquadratic growth

Dominic Breit, Martin Fuchs

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Abstract

We discuss partial regularity results concerning local minimizers u : R-3 superset of Omega -> R-3 of variational integrals of the form

integral(Omega) {h(|epsilon(w)|) - f.w} dx

defined on appropriate classes of solenoidal fields, where h is a N-function of rather general type. As a byproduct we obtain a theorem on partial C (1)-regularity for weak solutions of certain non-uniformly elliptic Stokes-type systems modelling generalized Newtonian fluids.

Original languageEnglish
Pages (from-to)371-385
Number of pages15
JournalJournal of Mathematical Fluid Mechanics
Volume13
Issue number3
DOIs
Publication statusPublished - Sep 2011

Keywords

  • Stokes problem
  • generalized Newtonian fluids
  • regularity
  • non-uniformly elliptic systems
  • slow flows
  • NON-NEWTONIAN FLUIDS
  • VARIATIONAL INTEGRALS
  • HIGHER INTEGRABILITY
  • REGULARITY

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