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

Yoshiyuki Kagei

Research output: Contribution to journalArticle

12 Citations (Scopus)

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 languageEnglish
Pages (from-to)1-31
Number of pages31
JournalJournal of Mathematical Fluid Mechanics
Volume13
Issue number1
DOIs
Publication statusPublished - Mar 1 2011

Fingerprint

Compressible Navier-Stokes Equations
Couette Flow
Couette flow
Asymptotic Behavior of Solutions
Navier-Stokes equation
Navier Stokes equations
disturbances
Disturbance
Sobolev space
Sobolev spaces
Asymptotically Stable
norms
Mach number
Heat Equation
Sobolev Spaces
Linear equation
Reynolds number
Norm
thermodynamics
Term

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.

In: Journal of Mathematical Fluid Mechanics, Vol. 13, No. 1, 01.03.2011, p. 1-31.

Research output: Contribution to journalArticle

@article{2359c6d3e83e4486a32677c1a01333ec,
title = "Asymptotic behavior of solutions of the compressible navier-stokes equation around the plane couette flow",
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.",
author = "Yoshiyuki Kagei",
year = "2011",
month = "3",
day = "1",
doi = "10.1007/s00021-009-0019-9",
language = "English",
volume = "13",
pages = "1--31",
journal = "Journal of Mathematical Fluid Mechanics",
issn = "1422-6928",
publisher = "Birkhauser Verlag Basel",
number = "1",

}

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 -