Hölder Continuous Solutions to the Three-dimensional Prandtl System

Abstract

Adapting the convex integration technique introduced by De Lellis and Sz{é}kelyhidi, we construct Hölder continuous weak solutions to the three dimensional Prandtl system and some other models with vertical viscosity.

References in corpus (3)

• On the ill-posedness of the Prandtl equation
• On the ill-posedness of the Prandtl equations in three space dimensions
• Well-posedness in Gevrey space for the Prandtl equations with non-degenerate critical points

Cited by in corpus (4)

• Magnetic effects on the solvability of 2D MHD boundary layer equations without resistivity in Sobolev spaces
• Well-posedness of the MHD boundary layer system in Gevrey function space without Structural Assumption
• Finite energy weak solution of 2d Boussinesq equation with diffusive temperature
• Hölder continuous weak solution of 2d Boussinesq equation with diffusive temperature