Remarks on High Reynolds Numbers Hydrodynamics and the Inviscid Limit

Peter Constantin, Vlad Vicol

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


We prove that any weak space-time L2 vanishing viscosity limit of a sequence of strong solutions of Navier–Stokes equations in a bounded domain of R2 satisfies the Euler equation if the solutions’ local enstrophies are uniformly bounded. We also prove that t- a. e. weak L2 inviscid limits of solutions of 3D Navier–Stokes equations in bounded domains are weak solutions of the Euler equation if they locally satisfy a scaling property of their second-order structure function. The conditions imposed are far away from boundaries, and wild solutions of Euler equations are not a priori excluded in the limit.

Original languageEnglish (US)
Pages (from-to)711-724
Number of pages14
JournalJournal of Nonlinear Science
Issue number2
StatePublished - Apr 1 2018

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • General Engineering
  • Applied Mathematics


  • Energy dissipation
  • Euler equations
  • Inviscid limit
  • Navier–Stokes equations


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