The Regularity of Weak Solutions of the 3D Navier-Stokes Equations in B^sub [INFINITY],[INFINITY]^^sup -1

We show that if a Leray-Hopf solution u of the three-dimensional Navier-Stokes equation belongs to C ( ( 0 , T ] ; B ∞ , ∞ − 1 ) or its jumps in the B ∞ , ∞ − 1 -norm do not exceed a constant multiple of viscosity, then u is regular for (0, T]. Our method uses frequency local estimates on the nonlin...

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Bibliographic Details
Published in:Archive for rational mechanics and analysis 2010-01, Vol.195 (1), p.159
Main Authors: Cheskidov, A, Shvydkoy, R
Format: Article
Language:English
Subjects:
Navier-Stokes equations
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Summary:We show that if a Leray-Hopf solution u of the three-dimensional Navier-Stokes equation belongs to C ( ( 0 , T ] ; B ∞ , ∞ − 1 ) or its jumps in the B ∞ , ∞ − 1 -norm do not exceed a constant multiple of viscosity, then u is regular for (0, T]. Our method uses frequency local estimates on the nonlinear term, and yields an extension of the classical Ladyzhenskaya-Prodi-Serrin criterion.[PUBLICATION ABSTRACT]
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-009-0265-2