Differential and Integral Equations

On the regularizing effect of the vorticity direction in incompressible viscous flows

Hugo Beirão da Veiga and Luigi C. Berselli

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We improve results in reference [6] concerning the effect of the direction of the vorticity on the regularity of weak solutions to the 3D Navier--Stokes equations. In particular, we prove that, if the direction of the vorticity belongs to suitable Sobolev spaces, then there exists a unique smooth solution of the Cauchy problem for the Navier--Stokes equations.

Article information

Differential Integral Equations, Volume 15, Number 3 (2002), 345-356.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10]
Secondary: 35B65: Smoothness and regularity of solutions 35Q35: PDEs in connection with fluid mechanics 76D03: Existence, uniqueness, and regularity theory [See also 35Q30] 76D05: Navier-Stokes equations [See also 35Q30]


Beirão da Veiga, Hugo; Berselli, Luigi C. On the regularizing effect of the vorticity direction in incompressible viscous flows. Differential Integral Equations 15 (2002), no. 3, 345--356. https://projecteuclid.org/euclid.die/1356060864

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