On the Spectral Properties for the Linearized Problem around Space-Time-Periodic States of the Compressible Navier–Stokes Equations

Mohamad Nor Azlan, Shota Enomoto and Yoshiyuki Kagei
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Mohamad Nor Azlan: Independent Researcher, Kuala Lumpur 56000, Malaysia
Shota Enomoto: General Education Department, National Institute of Technology, Toba College, Mie 517-8501, Japan
Yoshiyuki Kagei: Department of Mathematics, Tokyo Institute of Technology, Tokyo 152-8551, Japan

Mathematics, 2021, vol. 9, issue 7, 1-36

Abstract: This paper studies the linearized problem for the compressible Navier-Stokes equation around space-time periodic state in an infinite layer of R n ( n = 2 , 3 ), and the spectral properties of the linearized evolution operator is investigated. It is shown that if the Reynolds and Mach numbers are sufficiently small, then the asymptotic expansions of the Floquet exponents near the imaginary axis for the Bloch transformed linearized problem are obtained for small Bloch parameters, which would give the asymptotic leading part of the linearized solution operator as t ? ? .

Keywords: Compressible Navier–Stokes equation; infinite layer; periodic states; linearized stability; Floquet exponents (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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