## Journal of Mathematics of Kyoto University

- J. Math. Kyoto Univ.
- Volume 49, Number 2 (2009), 307-323.

### The relation between stationary and periodic solutions of the Navier-Stokes equations in two or three dimensional channels

#### Abstract

In this paper we will consider whether there exists a time periodic solution of the Navier-Stokes equations for infinite channels in $\mathbb{R}^n(n=2,3)$. H. Beirão da Veiga [4] treated such a problem. This paper is the special case of his paper and we argue the relation between the existence of stationary and time periodic solutions of the Navier-Stokes equations.

#### Article information

**Source**

J. Math. Kyoto Univ., Volume 49, Number 2 (2009), 307-323.

**Dates**

First available in Project Euclid: 22 October 2009

**Permanent link to this document**

https://projecteuclid.org/euclid.kjm/1256219158

**Digital Object Identifier**

doi:10.1215/kjm/1256219158

**Mathematical Reviews number (MathSciNet)**

MR2571843

**Zentralblatt MATH identifier**

1180.35414

**Subjects**

Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 76D05: Navier-Stokes equations [See also 35Q30]

#### Citation

Kobayashi, Teppei. The relation between stationary and periodic solutions of the Navier-Stokes equations in two or three dimensional channels. J. Math. Kyoto Univ. 49 (2009), no. 2, 307--323. doi:10.1215/kjm/1256219158. https://projecteuclid.org/euclid.kjm/1256219158