H\"{o}lder Continuous Solutions to the Three-dimensional Prandtl System

TL;DR

This paper constructs Hölder continuous weak solutions to the three-dimensional Prandtl system using convex integration, advancing understanding of boundary layer equations with vertical viscosity.

Contribution

It introduces a novel application of convex integration to produce Hölder continuous solutions for the 3D Prandtl system, a significant step in boundary layer theory.

Findings

Existence of Hölder continuous weak solutions to the 3D Prandtl system.

Application of convex integration to boundary layer equations.

Solutions demonstrate specific regularity properties.

Abstract

Adapting the convex integration technique introduced by De Lellis and Sz{\'e}kelyhidi, we construct H\"{o}lder continuous weak solutions to the three dimensional Prandtl system and some other models with vertical viscosity.