Blow ups of complex solutions of the 3D Navier-Stokes system and renormalization group method

Dong Li, Ya G. Sinai

Research output: Contribution to journalArticle

43 Scopus citations

Abstract

We consider complex-valued solutions of the three-dimensional Navier-Stokes system without external forcing on ℝ3. We show that there exists an open set in the space of 10-parameter families of initial conditions such that for each family from this set there are values of parameters for which the solution develops blow up in finite time.

Original languageEnglish (US)
Pages (from-to)267-313
Number of pages47
JournalJournal of the European Mathematical Society
Volume10
Issue number2
DOIs
StatePublished - Jan 1 2008

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Fixed point
  • Hermite polynomials
  • Linearization near a fixed point
  • Navier-Stokes system
  • Renormalization group theory
  • Spectrum of the linearized group

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