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 -