Anna L Mazzucato 2005 Nonlinearity 18 1 doi:10.1088/0951-7715/18/1/001
Anna L Mazzucato
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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.
35Q30 Stokes and Navier-Stokes equations (See also 76D05, 76D07, 76N10)
Issue 1 (January 2005)
Received 3 November 2003, in final form 5 July 2004
Published 24 September 2004
Anna L Mazzucato 2005 Nonlinearity 18 1
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