## Osaka Journal of Mathematics

### Asymptotic behavior of solutions to the compressible Navier-Stokes equation in a cylindrical domain

#### Abstract

Asymptotic behavior of solutions to the compressible Navier-Stokes equation around a given constant state is investigated on a cylindrical domain in $\mathbf{R}^{3}$, under the no slip boundary condition for the velocity field. The $L^{2}$ decay estimate is established for the perturbation from the constant state. It is also shown that the time-asymptotic leading part of the perturbation is given by a function satisfying a 1 dimensional heat equation. The proof is based on an energy method and asymptotic analysis for the associated linearized semigroup.

#### Article information

Source
Osaka J. Math., Volume 45, Number 4 (2008), 987-1026.

Dates
First available in Project Euclid: 26 November 2008

https://projecteuclid.org/euclid.ojm/1227708830

Mathematical Reviews number (MathSciNet)
MR2493967

Zentralblatt MATH identifier
1161.35038

Subjects
Secondary: 76N15: Gas dynamics, general

#### Citation

Kagei, Yoshiyuki; Nukumizu, Takumi. Asymptotic behavior of solutions to the compressible Navier-Stokes equation in a cylindrical domain. Osaka J. Math. 45 (2008), no. 4, 987--1026. https://projecteuclid.org/euclid.ojm/1227708830

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