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Gevrey stability of Prandtl expansions for 2-dimensional Navier-Stokes flows. (English) Zbl 1420.35187

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.
Reviewer: Cheng He (Beijing)

MSC:

35Q30 Navier-Stokes equations
35Q35 PDEs in connection with fluid mechanics
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76D05 Navier-Stokes equations for incompressible viscous fluids
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