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.

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U2 - 10.1007/s00021-009-0019-9

DO - 10.1007/s00021-009-0019-9

M3 - Article

AN - SCOPUS:84856300360

SN - 1422-6928

VL - 13

SP - 1

EP - 31

JO - Journal of Mathematical Fluid Mechanics

JF - Journal of Mathematical Fluid Mechanics

IS - 1

ER -