Well-posedness in Gevrey function space for 3D Prandtl equations without Structural Assumption

Abstract

We establish the well-posedness in Gevrey function space with optimal class of regularity 2 for the three dimensional Prandtl system without any structural assumption. The proof combines in a novel way a new cancellation in the system with some of the old ideas to overcome the difficulty of the loss of derivatives in the system.This shows that the three dimensional instabilities in the system leading to ill-posedness are not worse than the two dimensional ones.

References in corpus (3)

• Onsager's Conjecture with Physical Boundaries and an Application to the Vanishing Viscosity Limit
• A note on the Prandtl boundary layers
• On the zero-viscosity limit of the Navier-Stokes equations in the half-space

Cited by in corpus (4)

• Global-in-$x$ Stability of Steady Prandtl Expansions for 2D Navier-Stokes Flows
• Boundary Layer Expansions for the Stationary Navier-Stokes Equations
• Well-posedness of the MHD boundary layer system in Gevrey function space without Structural Assumption
• Well-posedness in Sobolev spaces of the two-dimensional MHD Boundary layer equations without viscosity