Water waves problem with surface tension in a corner domain I: A priori estimates with constrained contact angle

2017/09/01 by Ming Mei, Mei Ming, Chao Wang +2 · 2 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Aquatic and Environmental Studies #Arctic and Antarctic ice dynamics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #math-ph #math.AP #math.MP

paper · pdf · doi:10.48550/arxiv.1709.00180

37 pages, 1 figures

openalex publication_date 2017/09/01 · arxiv created 2020/04/20 · arxiv updated 2020/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the two dimensional water waves problem with surface tension in the case when there is a non-zero contact angle between the free surface and the bottom. In the presence of surface tension, dissipations take place at the contact point. Moreover, when the contact angle is less than π/6, no singularity appears in our settings. Using elliptic estimates in corner domains and a geometric approach, we prove an a priori estimate for the water waves problem.

Citations

• Well-posedness for the motion of an incompressible liquid with free surface boundary
• Well-posedness in Sobolev spaces of the full water wave problem in 2-D

Cited by

• Shallow water models for the dynamics of oscillating water columns
• The shoreline problem for the one-dimensional shallow water and Green-Naghdi equations

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