Optimal Prandtl expansion around concave boundary layer

Abstract

We provide an optimal Gevrey stability result for general boundary layer expansions, under a mild concavity condition on the boundary layer profile. Our result generalizes (and even improves in the non strictly concave case) the one obtained in [Gerard-Varet et al, Duke Math. J. 167 (2018)], restricted to expansions of shear flow type.

References in corpus (2)

• On the ill-posedness of the Prandtl equation
• On the analyticity and Gevrey class regularity up to the boundary for the Euler Equations

Cited by in corpus (7)

• On the Euler+Prandtl expansion for the Navier-Stokes equations
• Optimal Gevrey stability of hydrostatic approximation for the Navier-Stokes equations in a thin domain
• Global-in-$x$ Stability of Steady Prandtl Expansions for 2D Navier-Stokes Flows
• Boundary Layer Expansions for the Stationary Navier-Stokes Equations
• On the $L^{\infty }$ stability of Prandtl expansions in Gevrey class
• Well-posedness of the MHD boundary layer system in Gevrey function space without Structural Assumption
• Remarks on the Steady Prandtl Boundary Layer Expansions