Determining finite volume elements for the 2D Navier-Stokes equations

Don A. Jones, Edriss S. Titi

Research output: Contribution to journalArticle

57 Scopus citations

Abstract

We consider the 2D Navier-Stokes equations on a square with periodic boundary conditions. Dividing the square into N equal subsquares, we show that if the asymptotic behavior of the average of solutions on these subsquares (finite volume elements) is known, then the large time behavior of the solution itself is completely determined, provided N is large enough. We also establish a rigorous upper bound for N needed to determine the solutions to the Navier-Stokes equation in terms of the physical parameters of the problem.

Original languageEnglish (US)
Pages (from-to)165-174
Number of pages10
JournalPhysica D: Nonlinear Phenomena
Volume60
Issue number1-4
DOIs
StatePublished - Nov 1 1992
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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