# Asymptotic Behavior of the Semigroup Associated with the Linearized Compressible Navier–Stokes Equation in an Inﬁnite Layer

### Yoshiyuki Kagei

Kyushu University, Fukuoka, Japan

## Abstract

Asymptotic behavior of solutions to the linearized compressible Navier–Stokes equation around a given constant state is considered in an inﬁnite layer ℝ_n_−1 × (0, *a*), *n* ≥ 2, under the no slip boundary condition for the momentum. The *L__p* decay estimates of the associated semigroup are established for all 1 ≤ *p* ≤ ∞. It is also shown that the time-asymptotic leading part of the semigroup is given by an *n* − 1 dimensional heat semigroup.

## Cite this article

Yoshiyuki Kagei, Asymptotic Behavior of the Semigroup Associated with the Linearized Compressible Navier–Stokes Equation in an Inﬁnite Layer. Publ. Res. Inst. Math. Sci. 43 (2007), no. 3, pp. 763–794

DOI 10.2977/PRIMS/1201012041