Traveling Waves Bifurcating from Plane Poiseuille Flow of the Compressible Navier–Stokes Equation

Yoshiyuki Kagei, Takaaki Nishida

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Plane Poiseuille flow in viscous compressible fluid is known to be asymptotically stable if Reynolds number R and Mach number M are sufficiently small. On the other hand, for R and M being not necessarily small, an instability criterion for plane Poiseuille flow is known, and the criterion says that, when R increases, a pair of complex conjugate eigenvalues of the linearized operator cross the imaginary axis. In this paper it is proved that a spatially periodic traveling wave bifurcates from plane Poiseuille flow when the critical eigenvalues cross the imaginary axis.

Original languageEnglish
JournalArchive for Rational Mechanics and Analysis
Volume231
Issue number1
DOIs
Publication statusPublished - Jan 22 2019

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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