Maximal Double-Exponential Growth for the Euler Equation on the Half-Plane

TL;DR

This paper demonstrates that smooth solutions to the Euler equation on the half-plane can experience double-exponential growth in vorticity gradients, establishing the maximal growth rate and constructing solutions that achieve it, a first for unbounded 2D domains.

Contribution

It identifies the maximal possible growth rate of vorticity gradients and constructs solutions that attain this rate on the half-plane, advancing understanding of 2D Euler dynamics.

Findings

Double-exponential growth of vorticity gradients shown

Maximal growth rate determined and achieved

First such results on unbounded 2D domains

Abstract

We show that smooth solutions to the Euler equation on the half-plane can exhibit double-exponential growth of their vorticity gradients. We also determine the maximal possible growth rate and construct solutions that saturate it. These are the first such results on an unbounded resp. any 2D domain.