Low regularity well-posedness for two-dimensional deep gravity water waves with constant vorticity

2023/12/14 by Lizhe Wan, Wan, Lizhe
Earth and Planetary Sciences · Mathematics · #35Q31 #76B15 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Ocean Waves and Remote Sensing

paper · pdf · doi:10.48550/arxiv.2312.09347

openalex publication_date 2023/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the two dimensional gravity water waves with nonzero constant vorticity in infinite depth. We show that for s≥ (3)/(4), the water waves system is locally well-posed in H^s, which is the nonzero constant vorticity counterpart of the breakthrough work of Ai-Ifrim-Tataru in [4]. It is also a (1)/(4) improvement in Sobolev regularity compared to the previous result of Ifrim-Tataru in [17].

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