Negative Orlicz-Sobolev norms and strongly nonlinear systems in fluid mechanics

Dominic Breit, Andrea Cianchi

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We prove a version of the negative norm theorem in Orlicz-Sobolev spaces. A study of boundedness properties of the Bogovskiĭ operator between Orlicz spaces is a crucial step, of independent interest, in our approach. Applications to the problem of pressure reconstruction for non-Newtonian fluids governed by constitutive laws, which are not necessarily of power type, are presented. A key inequality for a numerical analysis of the underlying elliptic system is also derived.

Original languageEnglish
Pages (from-to)48-83
JournalJournal of Differential Equations
Volume259
Issue number1
DOIs
Publication statusPublished - 2014

Keywords

  • Bogovskiĭ operator
  • Negative norms
  • Non-Newtonian fluids
  • Orlicz-Sobolev spaces
  • Singular integrals
  • Strongly nonlinear elliptic systems

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