  In this paper, we prove the $L^\infty\cap L^2$ stability of Prandtl
expansions of shear flow type as $\big(U(y/\sqrt{\nu}),0\big)$ 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 introduced by Grenier, Guo and
Nguyen.
