Differential and Integral Equations

Regularity criteria in weak spaces for $3$-dimensional Navier-Stokes equations in terms of the pressure

Zhihui Cai, Jishan Fan, and Jian Zhai

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Abstract

In this paper we consider the Cauchy problem for the $3$-dimensional Navier-Stokes equations and we establish some Serrin-type regularity criterion in weak spaces involving the summability of the pressure or the gradient of the pressure.

Article information

Source
Differential Integral Equations, Volume 23, Number 11/12 (2010), 1023-1033.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019071

Mathematical Reviews number (MathSciNet)
MR2742476

Zentralblatt MATH identifier
1240.35380

Subjects
Primary: 35B65: Smoothness and regularity of solutions 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 76D05: Navier-Stokes equations [See also 35Q30]

Citation

Cai, Zhihui; Fan, Jishan; Zhai, Jian. Regularity criteria in weak spaces for $3$-dimensional Navier-Stokes equations in terms of the pressure. Differential Integral Equations 23 (2010), no. 11/12, 1023--1033. https://projecteuclid.org/euclid.die/1356019071


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