### Abstract

Asymptotic behavior of solutions to the compressible Navier-Stokes equation around the plane Couette flow is investigated. It is shown that the plane Couette flow is asymptotically stable for initial disturbances sufficiently small in some L ^{2} Sobolev space if the Reynolds and Mach numbers are sufficiently small. Furthermore, the disturbances behave in large time in L ^{2} norm as solutions of an n - 1 dimensional linear heat equation with a convective term.

Original language | English |
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Pages (from-to) | 1-31 |

Number of pages | 31 |

Journal | Journal of Mathematical Fluid Mechanics |

Volume | 13 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar 1 2011 |

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### All Science Journal Classification (ASJC) codes

- Mathematical Physics
- Condensed Matter Physics
- Computational Mathematics
- Applied Mathematics

### Cite this

**Asymptotic behavior of solutions of the compressible navier-stokes equation around the plane couette flow.** / Kagei, Yoshiyuki.

Research output: Contribution to journal › Article

*Journal of Mathematical Fluid Mechanics*, vol. 13, no. 1, pp. 1-31. https://doi.org/10.1007/s00021-009-0019-9

}

TY - JOUR

T1 - Asymptotic behavior of solutions of the compressible navier-stokes equation around the plane couette flow

AU - Kagei, Yoshiyuki

PY - 2011/3/1

Y1 - 2011/3/1

N2 - Asymptotic behavior of solutions to the compressible Navier-Stokes equation around the plane Couette flow is investigated. It is shown that the plane Couette flow is asymptotically stable for initial disturbances sufficiently small in some L 2 Sobolev space if the Reynolds and Mach numbers are sufficiently small. Furthermore, the disturbances behave in large time in L 2 norm as solutions of an n - 1 dimensional linear heat equation with a convective term.

AB - Asymptotic behavior of solutions to the compressible Navier-Stokes equation around the plane Couette flow is investigated. It is shown that the plane Couette flow is asymptotically stable for initial disturbances sufficiently small in some L 2 Sobolev space if the Reynolds and Mach numbers are sufficiently small. Furthermore, the disturbances behave in large time in L 2 norm as solutions of an n - 1 dimensional linear heat equation with a convective term.

UR - http://www.scopus.com/inward/record.url?scp=84856300360&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84856300360&partnerID=8YFLogxK

U2 - 10.1007/s00021-009-0019-9

DO - 10.1007/s00021-009-0019-9

M3 - Article

AN - SCOPUS:84856300360

VL - 13

SP - 1

EP - 31

JO - Journal of Mathematical Fluid Mechanics

JF - Journal of Mathematical Fluid Mechanics

SN - 1422-6928

IS - 1

ER -