## 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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### References:

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