Solenoidal Lipschitz truncation and applications in fluid mechanics

Dominic Breit, L. Diening, M. Fuchs

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

We extend the Lipschitz truncation method to the setting of solenoidal functions. In particular, we approximate a solenoidal Sobolev function by a solenoidal Lipschitz function which differs from the original function only on a small set.

Our main application is the existence of weak solutions to the two-dimensional Prandtl-Eyring fluid model which has almost linear growth. In this situation a correction via Bogovskii operators does not work.

Furthermore, we extend the concept of almost A-harmonicity to the fluid context in the pressure free formulation. (C) 2012 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)1910-1942
Number of pages33
JournalJournal of Differential Equations
Volume253
Issue number6
DOIs
Publication statusPublished - 15 Sep 2012

Keywords

  • Solenoidal Lipschitz truncation
  • Divergence free truncation
  • Navier-Stokes
  • Generalized Newtonian fluids
  • Prandtl-Eyring fluid
  • A-harmonic approximation
  • GENERAL BOUNDARY CONDITIONS
  • EQUATIONS
  • APPROXIMATION
  • PLASTICITY
  • REGULARITY
  • VISCOSITY
  • EXISTENCE
  • LAW

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