Absence of the local existence theorem in the critical space for the 3D-Navier-Stokes system

Research output: Contribution to journalArticle

Abstract

We consider the 3D-Navier-Stokes System (NSS) on R3 without external forcing. After Fourier transform we get a nonlocal nonlinear integral equation equivalent to NSS. For one-parameter families of initial conditions A · c(0)(k)/|k|2 in the case of small |A| the NSS has a unique global solution. We argue that for large A NSS has no local solutions with these initial conditions.

Original languageEnglish (US)
Pages (from-to)3635-3637
Number of pages3
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume15
Issue number11
DOIs
StatePublished - Nov 2005

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics

Keywords

  • Critical space
  • Fourier transform
  • Navier-Stokes system

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