Minimal L3-initial data for potential navier-stokes singularities

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Abstract

We give a simple proof of the existence of initial data with minimal L 3-norm for potential Navier-Stokes singularities, recently established in [I. Gallagher, G. S. Koch, and F. Planchon, Math. Ann., 355 (2013), pp. 1527-1559] with techniques based on profile decomposition. Our proof is more elementary and is based on suitable splittings of initial data and energy methods. The main difficulty in the L3 case is the lack of compactness of the embedding L3 loc → L2 loc.

Original languageEnglish (US)
Pages (from-to)1448-1459
Number of pages12
JournalSIAM Journal on Mathematical Analysis
Volume45
Issue number3
DOIs
StatePublished - 2013

Keywords

  • Blow-up solutions
  • Navier-Stokes equations
  • Weak solution

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