## Hiroshima Mathematical Journal

- Hiroshima Math. J.
- Volume 38, Number 1 (2008), 95-124.

### Large time behavior of solutions to the compressible Navier-Stokes equation in an infinite layer

#### Abstract

Large time behavior of solutions to the compressible Navier-Stokes equation around a given constant state is considered in an infinite layer ${\bf R}^{n-1}\times (0,a)$, $n\geq2$, under the no slip boundary condition for the velocity. The $L^p$ decay estimates of the solution are established for all $1\leq p\leq \infty$. It is also shown that the time-asymptotic leading part of the solution is given by a function satisfying the $n-1$ dimensional heat equation. The proof is given by combining a weighted energy method with time-weight functions and the decay estimates for the associated linearized semigroup

#### Article information

**Source**

Hiroshima Math. J., Volume 38, Number 1 (2008), 95-124.

**Dates**

First available in Project Euclid: 7 April 2008

**Permanent link to this document**

https://projecteuclid.org/euclid.hmj/1207580346

**Digital Object Identifier**

doi:10.32917/hmj/1207580346

**Mathematical Reviews number (MathSciNet)**

MR2397381

**Zentralblatt MATH identifier**

1151.35072

**Subjects**

Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 76N15: Gas dynamics, general

**Keywords**

compressible Navier-Stokes equation asymptotic behavior infinite layer

#### Citation

Kagei, Y. Large time behavior of solutions to the compressible Navier-Stokes equation in an infinite layer. Hiroshima Math. J. 38 (2008), no. 1, 95--124. doi:10.32917/hmj/1207580346. https://projecteuclid.org/euclid.hmj/1207580346