Preprint Traveling waves bifurcating from plane Poiseuille flow of the compressible Navier-Stokes equation

Kagei, Yoshiyuki  ,  Nishida, Takaaki

2015-92015-10-16 , Faculty of Mathematics, Kyushu University
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 ow when the critical eigenvalues cross the imaginary axis.

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