Gevrey stability of Prandtl expansions for 2-dimensional Navier-Stokes flows (Q1615255)

The authors study the Gevrey stability of Prandtl expansions for two-dimensional Navier-Stokes flows. Under the assumption that the corrector of a shear flow solutions of Prandtl type is monotonic and concave in $y$, the shear flow solution is stable in some interval, under the perturbations with Gevrey regularity in $x$ and Sobolev regularity in $y$, which improve the known results. The new ingredient of the arguments is to establish a sharp resolvent estimates for the linearized Orr-Sommerfeld operator.