TY - JOUR
T1 - Stability of plane Couette flows with respect to small periodic perturbations
AU - Heck, Horst
AU - Kim, Hyunseok
AU - Kozono, Hideo
N1 - Funding Information:
The first author was supported by Japan Society for the Promotion of Science. The second author was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund) (KRF-2006-331-C00023).
PY - 2009/11/1
Y1 - 2009/11/1
N2 - We consider the plane Couette flow v0 = (xn, 0, ..., 0) in the infinite layer domain Ω = Rn - 1 × (- 1, 1), where n ≥ 2 is an integer. The exponential stability of v0 in Ln is shown under the condition that the initial perturbation is periodic in (x1, ..., xn - 1) and sufficiently small in the Ln-norm.
AB - We consider the plane Couette flow v0 = (xn, 0, ..., 0) in the infinite layer domain Ω = Rn - 1 × (- 1, 1), where n ≥ 2 is an integer. The exponential stability of v0 in Ln is shown under the condition that the initial perturbation is periodic in (x1, ..., xn - 1) and sufficiently small in the Ln-norm.
KW - Plane Couette flow
KW - Stability
KW - The Navier-Stokes equations
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U2 - 10.1016/j.na.2009.02.034
DO - 10.1016/j.na.2009.02.034
M3 - Article
AN - SCOPUS:67349166105
SN - 0362-546X
VL - 71
SP - 3739
EP - 3758
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
IS - 9
ER -