Strong continuity for the 2D Euler equations

TL;DR

This paper establishes strong continuity results for bounded solutions to the 2D Euler equations, demonstrating sequential continuity for general solutions and uniform continuity for H"older continuous solutions.

Contribution

It introduces new strong continuity theorems for the 2D Euler equations, differentiating between general bounded solutions and H"older continuous solutions.

Findings

Sequential continuity for bounded solutions.

Uniform continuity for H"older continuous solutions.

Enhanced understanding of solution stability in Euler equations.

Abstract

We prove two results of strong continuity with respect to the initial datum for bounded solutions to the Euler equations in vorticity form. The first result provides sequential continuity and holds for a general bounded solution. The second result provides uniform continuity and is restricted to H\"older continuous solutions.