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

Yoshiyuki Kagei, Takaaki Nishida

    Research output: Contribution to journalArticlepeer-review

    4 Citations (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
    Pages (from-to)1-44
    Number of pages44
    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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