Low regularity well-posedness for two-dimensional hydroelastic waves

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 $s>\frac{3}{4}$.

62 pages, 1 figure