The Navier-Stokes equations on a bounded domain

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Abstract

Suppose U is an open bounded subset of 3-space such that the boundary of U has Lebesgue measure zero. Then for any initial condition with finite kinetic energy we can find a global (i.e. for all time) weak solution u to the time dependent Navier-Stokes equations of incompressible fluid flow in U such that the curl of u is continuous outside a locally closed set whose 5/3 dimensional Hausdorff measure is finite.

Original languageEnglish (US)
Pages (from-to)1-42
Number of pages42
JournalCommunications In Mathematical Physics
Volume73
Issue number1
DOIs
StatePublished - May 1980

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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