Local well-posedness of the capillary-gravity water waves with acute contact angles

2021/12/28 by Chao Wang, Ming, Mei, Wang, Chao · 1 citation
Earth and Planetary Sciences · Mathematics · #Analysis of PDEs (math.AP) #Arctic and Antarctic ice dynamics #FOS: Mathematics #Navier-Stokes equation solutions #Ocean Waves and Remote Sensing

paper · pdf · doi:10.48550/arxiv.2112.14001

openalex publication_date 2021/12/28 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We consider the two-dimensional capillary-gravity water waves problem where the free surface Γ_t intersects the bottom Γ_b at two contact points. In our previous works \citeMW2, MW3, the local well-posedness for this problem has been proved with the contact angles less than π/16. In this paper, we study the case where the contact angles belong to (0, π/2). It involves much worse singularities generated from corresponding elliptic systems, which have a strong influence on the regularities for the free surface and the velocity field. Combining the theory of singularity decompositions for elliptic problems with the structure of the water waves system, we obtain a priori energy estimates. Based on these estimates, we also prove the local well-posedness of the solutions in a geometric formulation.

Cited by

• Shallow water models for the dynamics of oscillating water columns

Related

• Low regularity well-posedness for two-dimensional deep water waves
• Local Well-Posedness of the Gravity-Capillary Water Waves System in the Presence of Geometry and Damping
• Improved low regularity theory for gravity-capillary waves
• Water waves problem with surface tension in a corner domain II: the local well-posednes
• Angled crested like water waves with surface tension: Wellposedness of the problem