Spectral properties of the linearized compressible Navier-Stokes equation around time-periodic parallel flow

The linearized problem around a time-periodic parallel flow of the compressible Navier-Stokes equation in an infinite layer is investigated. By using the Floquet theory, spectral properties of the evolution operator associated with the linearized problem are studied in detail. The Floquet representation of a low frequency part of the evolution operator, which plays an important role in the study of the nonlinear problem, is obtained.