Open Access
April, 2007 On the Regularity Conditions for the Navier-Stokes and Related Equations
Dongho Chae
Rev. Mat. Iberoamericana 23(1): 371-384 (April, 2007).


We obtain a regularity conditions for solutions of the 3D Navier-Stokes equations with fractional powers of the Laplacian, which incorporates the vorticity direction and its magnitude simultaneously. We find that regularity assumption of direction field of the vorticity compensates with the integrability condition for the magnitude of vorticity. The regularity of direction field is most naturally measured in terms of the Triebel-Lizorkin type of norms. This unifies and extends previous results in this direction of studies, where the geometric structure of the vortex stretching term is used to obtain refined regularity conditions, initiated by Constantin and Fefferman.


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Dongho Chae. "On the Regularity Conditions for the Navier-Stokes and Related Equations." Rev. Mat. Iberoamericana 23 (1) 371 - 384, April, 2007.


Published: April, 2007
First available in Project Euclid: 1 June 2007

zbMATH: 1130.35100
MathSciNet: MR2351138

Primary: 35Q30 , 76D03 , 76D05

Keywords: Navier-Stokes equations , regularity conditions , Triebel-Lizorkin type of spaces

Rights: Copyright © 2007 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.23 • No. 1 • April, 2007
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