Differential and Integral Equations

A new regularity criterion for steady Navier-Stokes equations

Jens Frehse and Michael Růžička

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We show that every weak solution $\mathbf{u}$ of the steady Navier--Stokes equations in a bounded domain $\Omega \subseteq \mathbb{R}^N$, $N\ge 5$, satisfying additionally $\mathbf{u}\in L^q(\Omega )$, where $ q\ge 4$ and $q > N/2$ (for the Dirichlet problem) or $ q\ge 4$ and $q > N/4$ (for the space periodic problem), is regular.

Article information

Differential Integral Equations, Volume 11, Number 2 (1998), 361-368.

First available in Project Euclid: 30 April 2013

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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 76D03: Existence, uniqueness, and regularity theory [See also 35Q30] 76D05: Navier-Stokes equations [See also 35Q30]


Frehse, Jens; Růžička, Michael. A new regularity criterion for steady Navier-Stokes equations. Differential Integral Equations 11 (1998), no. 2, 361--368. https://projecteuclid.org/euclid.die/1367341076

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