## Journal of the Mathematical Society of Japan

- J. Math. Soc. Japan
- Volume 55, Number 3 (2003), 797-826.

### On the steady flow of compressible viscous fluid and its stability with respect to initial disturbance

Yoshihiro SHIBATA and Koumei TANAKA

#### Abstract

We consider a compressible viscous fluid effected by general form external force in $R^{3}$. In part 1, an analysis of the linearized problem based on the weighted- $L_{2}$ method implies a condition on the external force for the existence and some regularities of the steady flow. In part 2, we study the stability of the steady flow with respect to the initial disturbance. What we proved is: if $H^{3}$-norm of the initial disturbance is small enough, then the solution to the non-stationary problem exists uniquely and globally in time.

#### Article information

**Source**

J. Math. Soc. Japan Volume 55, Number 3 (2003), 797-826.

**Dates**

First available in Project Euclid: 3 October 2007

**Permanent link to this document**

http://projecteuclid.org/euclid.jmsj/1191419003

**Digital Object Identifier**

doi:10.2969/jmsj/1191419003

**Mathematical Reviews number (MathSciNet)**

MR1978223

**Zentralblatt MATH identifier**

1051.76058

**Subjects**

Primary: 76N10: Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30]

Secondary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 34D99: None of the above, but in this section

**Keywords**

compressible fluid Navier-Stokes equation stationary solution stability

#### Citation

SHIBATA, Yoshihiro; TANAKA, Koumei. On the steady flow of compressible viscous fluid and its stability with respect to initial disturbance. J. Math. Soc. Japan 55 (2003), no. 3, 797--826. doi:10.2969/jmsj/1191419003. http://projecteuclid.org/euclid.jmsj/1191419003.