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

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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.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of MathematicsKyushu UniversityFukuokaJapan
  2. 2.Department of Advanced Mathematical SciencesKyoto UniversityKyotoJapan

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