On the analyticity and Gevrey class regularity up to the boundary for the Euler Equations

TL;DR

This paper proves that solutions to the 3D Euler equations in Gevrey-class bounded domains maintain their regularity up to the boundary, providing explicit decay estimates for the Gevrey radius.

Contribution

It establishes the Gevrey-class persistence of Euler solutions up to the boundary with explicit regularity decay estimates using Lagrangian coordinates.

Findings

Gevrey-class regularity persists up to the boundary

Explicit decay rate of Gevrey regularity radius derived

Lagrangian coordinates are used for analysis

Abstract

We consider the Euler equations in a three-dimensional Gevrey-class bounded domain. Using Lagrangian coordinates we obtain the Gevrey-class persistence of the solution, up to the boundary, with an explicit estimate on the rate of decay of the Gevrey-class regularity radius.