Lagrangian time-analyticity for the Euler equations in a Sobolev domain

TL;DR

This paper proves that Lagrangian trajectories of solutions to the Euler equations are time-analytic even when the domain has only Sobolev regularity, extending previous results to less regular domains.

Contribution

It establishes time-analyticity of Lagrangian trajectories for Euler solutions in Sobolev domains, a significant generalization over classical smooth domain assumptions.

Findings

Lagrangian trajectories are time-analytic in Sobolev domains

Extends analyticity results to less regular domains

Provides new insights into Euler equations in Sobolev settings

Abstract

Assuming only Sobolev regularity of the domain, we prove time-analyticity of Lagrangian trajectories for solutions of the Euler equations.