Spectral properties of the linearized semigroup of the compressible Navier-stokes equation on a periodic layer

The linearized problem for the compressible Navier-Stokes equation around a given con- stant state is considered in a periodic layer of ℝⁿ with n ≥ 2, and spectral properties of the linearized semigroup are investigated. It is shown that the linearized operator gener- ates a C₀-semigroup in L² over the periodic layer and the time-asymptotic leading part of the semigroup is given by a C₀-semigroup generated by an n – 1-dimensional elliptic operator with constant coefficients that are determined by solutions of a Stokes system over the basic period domain.