TY - JOUR

T1 - Traveling Waves Bifurcating from Plane Poiseuille Flow of the Compressible Navier–Stokes Equation

AU - Kagei, Yoshiyuki

AU - Nishida, Takaaki

N1 - Funding Information:
Acknowledgements. Y. sc Kagei was partly supported by JSPS KAKENHI Grant Numbers 24340028, 22244009, 24224003, 15K13449, 16H03947 and 16H06339. T. Nishida was partly supported by JSPS KAKENHI Grant Numbers 26400163 and 17K05317. The authors would like to thank the referee for his/her carefully reading the earlier version of the paper and giving valuable comments.
Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2019/1/22

Y1 - 2019/1/22

N2 - 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.

AB - 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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U2 - 10.1007/s00205-018-1269-6

DO - 10.1007/s00205-018-1269-6

M3 - Article

AN - SCOPUS:85048523175

VL - 231

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

SN - 0003-9527

IS - 1

ER -