Remarks on the Emergence of Weak Euler Solutions in the Vanishing Viscosity Limit

Theodore D. Drivas, Huy Q. Nguyen

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

We prove that if the local second-order structure function exponents in the inertial range remain positive uniformly in viscosity, then any spacetime L 2 weak limit of Leray–Hopf weak solutions of the Navier–Stokes equations on any bounded domain Ω ⊂ R d , d= 2 , 3 is a weak solution of the Euler equations. This holds for both no-slip and Navier friction conditions with viscosity-dependent slip length. The result allows for the emergence of non-unique, possibly dissipative, limiting weak solutions of the Euler equations.

Original languageEnglish (US)
Pages (from-to)709-721
Number of pages13
JournalJournal of Nonlinear Science
Volume29
Issue number2
DOIs
StatePublished - Apr 15 2019

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Engineering(all)
  • Applied Mathematics

Keywords

  • Euler equations
  • Inviscid limit
  • Navier-Stokes equations
  • Weak solutions

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