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

Authors：Chen, Qi; Wu, Di; Zhang, Zhifei^*

Source：Science China Mathematics, 2022, 65(12): 2521-2562.

DOI：10.1007/s11425-021-1896-5

• Navier-Stokes equations
• shear flow
• Prandtl expansion

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.

• Institution
  北京大学