Convergence of the vanishing viscosity approximation for superpositions of confined eddies

M. C. Lopes Filho, H. J. Nussenzveig Lopes, Yuxi Zheng

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

A confined eddy is a circularly symmetric flow with vorticity of compact support and zero net circulation. Confined eddies with disjoint supports can be super-imposed to generate stationary weak solutions of the two-dimensional incompressible inviscid Euler equations. In this work, we consider the unique weak solution of the two-dimensional incompressible Navier-Stokes equations having a disjoint superposition of very singular confined eddies as the initial datum. We prove the convergence of these weak solutions back to the initial configuration, as the Reynolds number goes to infinity. This implies that the stationary superposition of confined eddies with disjoint supports is the unique physically correct weak solution of the two-dimensional incompressible Euler equations.

Original languageEnglish (US)
Pages (from-to)291-304
Number of pages14
JournalCommunications In Mathematical Physics
Volume201
Issue number2
DOIs
StatePublished - Jan 1 1999

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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