On the L∞ stability of Prandtl expansions in the Gevrey class

摘要

In this paper, we prove the L-infinity boolean AND L-2 stability of Prandtl expansions of the shear flow type as (U(y/root nu), 0) for the initial perturbation in the Gevrey class, where U(y) is a monotone and concave function and nu is the viscosity coefficient. To this end, we develop the direct resolvent estimate method for the linearized Orr-Sommerfeld operator instead of the Rayleigh-Airy iteration method. Our method could be applied to the other relevant problems of hydrodynamic stability.

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