Asymptotic Behavior of Solutions to the Compressible Navier-Stokes Equation Around a Parallel Flow

Yoshiyuki Kagei

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)

Abstract

The initial boundary value problem for the compressible Navier-Stokes equation is considered in an infinite layer of R 2. It is proved that if the Reynolds and Mach numbers are sufficiently small, then strong solutions to the compressible Navier-Stokes equation around parallel flows exist globally in time for sufficiently small initial perturbations. The large time behavior of the solution is described by a solution of a one-dimensional viscous Burgers equation. The proof is given by a combination of spectral analysis of the linearized operator and a variant of the Matsumura-Nishida energy method.

Original languageEnglish
Pages (from-to)585-650
Number of pages66
JournalArchive for Rational Mechanics and Analysis
Volume205
Issue number2
DOIs
Publication statusPublished - Aug 2012

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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