### Abstract

Stability of parallel flow of the compressible Navier-Stokes equation in a cylindrical domain is studied. It is shown that if the Reynolds and Mach numbers are sufficiently small, then parallel flow is asymptotically stable and the asymptotic leading part of the disturbances is described by a one dimensional viscous Burgers equation.

Original language | English |
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Pages (from-to) | 362-396 |

Number of pages | 35 |

Journal | Nonlinear Analysis, Theory, Methods and Applications |

Volume | 127 |

DOIs | |

Publication status | Published - Aug 14 2015 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

**Large time behavior of solutions to the compressible Navier-Stokes equations around a parallel flow in a cylindrical domain.** / Aoyama, Reika; Kagei, Yoshiyuki.

Research output: Contribution to journal › Article

*Nonlinear Analysis, Theory, Methods and Applications*, vol. 127, pp. 362-396. https://doi.org/10.1016/j.na.2015.07.009

}

TY - JOUR

T1 - Large time behavior of solutions to the compressible Navier-Stokes equations around a parallel flow in a cylindrical domain

AU - Aoyama, Reika

AU - Kagei, Yoshiyuki

PY - 2015/8/14

Y1 - 2015/8/14

N2 - Stability of parallel flow of the compressible Navier-Stokes equation in a cylindrical domain is studied. It is shown that if the Reynolds and Mach numbers are sufficiently small, then parallel flow is asymptotically stable and the asymptotic leading part of the disturbances is described by a one dimensional viscous Burgers equation.

AB - Stability of parallel flow of the compressible Navier-Stokes equation in a cylindrical domain is studied. It is shown that if the Reynolds and Mach numbers are sufficiently small, then parallel flow is asymptotically stable and the asymptotic leading part of the disturbances is described by a one dimensional viscous Burgers equation.

UR - http://www.scopus.com/inward/record.url?scp=84939213038&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84939213038&partnerID=8YFLogxK

U2 - 10.1016/j.na.2015.07.009

DO - 10.1016/j.na.2015.07.009

M3 - Article

AN - SCOPUS:84939213038

VL - 127

SP - 362

EP - 396

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

ER -