Stability of plane Couette flows with respect to small periodic perturbations

摘要

We consider the plane Couette f10w Vo (Xn, 0, ..., 0) in the infinite layer domain {} = Rn- J x (一1 ， 1), where n~2 is an integer.ηle exponential stability of Vo in Ln is shown under the condition that the initial perturbation is periodic in (xJ , .. ., Xn-J) and sumciently small in the Ln-norm.