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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Communicated by T.-P. Liu
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Kagei, Y., Nishida, T. Traveling Waves Bifurcating from Plane Poiseuille Flow of the Compressible Navier–Stokes Equation. Arch Rational Mech Anal 231, 1–44 (2019). https://doi.org/10.1007/s00205-018-1269-6
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DOI: https://doi.org/10.1007/s00205-018-1269-6