TY - JOUR

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

AU - Kagei, Yoshiyuki

N1 - Funding Information:
This work was partially supported by Grant-in Aid for Scientific Research (B) No. 19340033 from the Japan Society for the Promotion of Science.

PY - 2011/3

Y1 - 2011/3

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 -