Differential and Integral Equations

On a regularity criterion for the solutions to the 3D Navier-Stokes equations

Luigi C. Berselli

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In this paper we give a simple proof of the regularity of a class of solutions to the 3D Navier-Stokes equations for a fluid filling {any} smooth three-dimensional domain. The regularity in the same class was proved by Beir\~ao da Veiga in reference [3], for the Cauchy problem in $\mathbb R^n.$

Article information

Differential Integral Equations, Volume 15, Number 9 (2002), 1129-1137.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q35: PDEs in connection with fluid mechanics
Secondary: 35B65: Smoothness and regularity of solutions 35D10 76D03: Existence, uniqueness, and regularity theory [See also 35Q30] 76D05: Navier-Stokes equations [See also 35Q30]


Berselli, Luigi C. On a regularity criterion for the solutions to the 3D Navier-Stokes equations. Differential Integral Equations 15 (2002), no. 9, 1129--1137. https://projecteuclid.org/euclid.die/1356060766

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