Existence and stability of time periodic solution to the compressible Navier-Stokes equation for time periodic external force with symmetry

Yoshiyuki Kagei, Kazuyuki Tsuda

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

Time periodic problem for the compressible Navier-Stokes equation for barotropic flow on the whole space is studied. The existence of a time periodic solution is proved for sufficiently small time periodic external force with some symmetry when the space dimension is greater than or equal to 3. The proof is based on the spectral properties of the time-. T-map associated with the linearized problem around the motionless state with constant density in some weighted Sobolev space. The stability of the time periodic solution is also proved and the decay estimate of the perturbation is established.

Original languageEnglish
Pages (from-to)399-444
Number of pages46
JournalJournal of Differential Equations
Volume258
Issue number2
DOIs
Publication statusPublished - Jan 1 2015

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Time-periodic Solutions
Sobolev spaces
Compressible Navier-Stokes Equations
Navier Stokes equations
Symmetry
Periodic Problem
Weighted Sobolev Spaces
Decay Estimates
Spectral Properties
Perturbation

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

Existence and stability of time periodic solution to the compressible Navier-Stokes equation for time periodic external force with symmetry. / Kagei, Yoshiyuki; Tsuda, Kazuyuki.

In: Journal of Differential Equations, Vol. 258, No. 2, 01.01.2015, p. 399-444.

Research output: Contribution to journalArticle

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