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

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.

Automated summary

This paper proves the stability of Prandtl expansions of the shear flow type and introduces a direct resolvent estimate method, which could be applied to other relevant problems of hydrodynamic stability.