Journal of the Mathematical Society of Japan

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

Yoshihiro SHIBATA and Koumei TANAKA

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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.


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