Improved low regularity theory for gravity-capillary waves

2023/08/30 by Ai, Albert
#76B03 #76B15 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.16176

Abstract

This article concerns the Cauchy problem for the gravity-capillary water waves system in general dimensions. We establish local well-posedness for initial data in H^s, with s > (d)/(2) + 2 - μ, with μ= (3)/(14) and μ= \frac37 in the cases d = 1 and d ≥ 2 respectively. This represents an improvement over the the state-of-the-art low regularity theory in d ≥ 2 dimensions.

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