On the energy spectrum for weak solutions of the Navier-stokes equations

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We consider the decay at high wavenumbers of the energy spectrum for weak solutions to the three-dimensional forced Navier-Stokes equation in the whole space. We observe that known regularity criteria imply that solutions are regular if the energy density decays at a sufficiently fast rate. This result applies also to a class of solutions with infinite global energy by localizing the Navier-Stokes equation. We consider certain modified Leray backward self-similar solutions, which belong to this class, and show that their energy spectrum decays at the critical rate for regularity. Therefore, this rate of decay is consistent with the appearance of an isolated self-similar singularity.

Original languageEnglish (US)
Pages (from-to)1-19
Number of pages19
JournalNonlinearity
Volume18
Issue number1
DOIs
StatePublished - Jan 1 2005

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Energy Spectrum
Navier-Stokes equation
Navier Stokes equations
Weak Solution
Navier-Stokes Equations
energy spectra
Decay
decay
regularity
Regularity Criterion
Self-similar Solutions
Energy Density
flux density
Regularity
Singularity
Imply
Three-dimensional
Energy
Class
energy

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

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On the energy spectrum for weak solutions of the Navier-stokes equations. / Mazzucato, Anna L.

In: Nonlinearity, Vol. 18, No. 1, 01.01.2005, p. 1-19.

Research output: Contribution to journalArticle

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