The Domain of Analyticity of Solutions to the Three-Dimensional Euler Equations in a Half Space

TL;DR

This paper investigates the analyticity properties of solutions to the 3D Euler equations in a half space, providing new decay estimates for the analyticity radius and establishing persistence of Gevrey-class regularity.

Contribution

It offers improved decay estimates for the analyticity radius and proves the persistence of Gevrey-class regularity for Euler solutions in a half space.

Findings

Decay rate of analyticity radius characterized by exponential integral of gradient norm

Persistence of Gevrey-class regularity established

Explicit decay rate of Gevrey regularity radius derived

Abstract

We address the problem of analyticity up to the boundary of solutions to the Euler equations in the half space. We characterize the rate of decay of the real-analyticity radius of the solution $u(t)$ in terms of $\exp{\int_{0}^{t} \Vert \nabla u(s) \Vert_{L^\infty} ds}$, improving the previously known results. We also prove the persistence of the sub-analytic Gevrey-class regularity for the Euler equations in a half space, and obtain an explicit rate of decay of the radius of Gevrey-class regularity.