### 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 language | English |
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Journal | Archive for Rational Mechanics and Analysis |

Volume | 231 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 22 2019 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Mathematics (miscellaneous)
- Mechanical Engineering

### Cite this

**Traveling Waves Bifurcating from Plane Poiseuille Flow of the Compressible Navier–Stokes Equation.** / Kagei, Yoshiyuki; Nishida, Takaaki.

Research output: Contribution to journal › Article

*Archive for Rational Mechanics and Analysis*, vol. 231, no. 1. https://doi.org/10.1007/s00205-018-1269-6

}

TY - JOUR

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

AU - Kagei, Yoshiyuki

AU - Nishida, Takaaki

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.

UR - http://www.scopus.com/inward/record.url?scp=85048523175&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85048523175&partnerID=8YFLogxK

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 -