## Differential and Integral Equations

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

### A new regularity criterion for steady Navier-Stokes equations

Jens Frehse and Michael Růžička

#### Abstract

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

**Source**

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

**Dates**

First available in Project Euclid: 30 April 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1367341076

**Mathematical Reviews number (MathSciNet)**

MR1741851

**Zentralblatt MATH identifier**

1008.35048

**Subjects**

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]

#### Citation

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