Low regularity well-posedness for two-dimensional hydroelastic waves

TL;DR

This paper proves that two-dimensional irrotational deep hydroelastic waves are locally well-posed in low regularity Sobolev spaces, specifically for regularity levels above 3/4, by constructing a modified energy functional.

Contribution

It extends low regularity well-posedness results to hydroelastic waves using a paradifferential energy approach, building on prior methods by Ifrim-Tataru and Ai-Ifrim-Tataru.

Findings

Well-posedness established for s > 3/4

Construction of a cubic modified energy functional

Application of paradifferential calculus techniques

Abstract

We investigate the low regularity local well-posedness of two-dimensional irrotational deep hydroelastic waves. Building on the approach of Ifrim-Tataru [29] and Ai-Ifrim-Tataru [5], in particular by constructing a cubic modified energy that incorporates a paradifferential weight chosen carefully, we prove that the hydroelastic waves are locally well-posed in $\mathcal{H}^s$ for $s>\frac{3}{4}$.