## Revista Matemática Iberoamericana

### On the Regularity Conditions for the Navier-Stokes and Related Equations

Dongho Chae

#### Abstract

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.

#### Article information

Source
Rev. Mat. Iberoamericana, Volume 23, Number 1 (2007), 371-384.

Dates
First available in Project Euclid: 1 June 2007

https://projecteuclid.org/euclid.rmi/1180728897

Mathematical Reviews number (MathSciNet)
MR2351138

Zentralblatt MATH identifier
1130.35100

Subjects
Primary: 35Q30 76D03 76D05

#### Citation

Chae, Dongho. On the Regularity Conditions for the Navier-Stokes and Related Equations. Rev. Mat. Iberoamericana 23 (2007), no. 1, 371--384. https://projecteuclid.org/euclid.rmi/1180728897

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