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

Abstract

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 low frequency part of the evolution operator, which plays an important role in the study of the nonlinear problem, is obtained.

Time periodic solutions to the three--dimensional equations of compressible magnetohydrodynamic flows

“…When there is no electromagnetic field, system (1) reduces to the compressible Navier-Stokes equations, cf. [1,2,10,13,14,15,19,20,23] and references therein. Here we only mention some of them related to our paper.…”

Time-periodic solutions of the compressible Navier–Stokes equations in $${\mathbb{R}^{4}}$$ R 4

“…In this work, the authors used the energy method and the spectral analysis for the optimal decay estimates on the linearized problem to establish the existence, but unfortunately, even using the optimal decay estimates, the existence can be proved only when the space dimension N ≥ 5. In a recent work [1,2], Bȓezina and Kagei considered the time-periodic parallel flow in a N-dimensional infinite layer R N −1 × (0, l), in the papers, by using the solution of a one-dimensional heat-type equation in a bounded domain (0, l), and the authors constructed a periodic solution for the Navier-Stokes equations with a special time-periodic external force of this form f = (f 1 (x n , t), 0, . .…”

Time‐periodic solution to the compressible nematic liquid crystal flows in periodic domain

“…It is worth mentioning that when d is a constant vector field, system reduces to the compressible Navier‐Stokes equation. There are some excellent works related to the periodic solutions, see previous studies and the references therein. Here, we only mention some of them for unbounded domain.…”