Work

A priori estimates for the moving contact line problem for the 2D nonlinear shallow water equations with a partially immersed obstacle

Year: 2026

Type: article

Abstract: We consider the initial value problem for the 2 D nonlinear shallow water model in the presence of a fixed partially immersed solid body. In this problem, we have a contact line where the solid body, the water, and the air meet, and whose projection on the horizontal plane moves freely even if the solid body is fixed. This wave-structure interaction problem reduces to an initial boundary value problem for the nonlinear shallow water equations in an exterior domain with a free boundary, for which we prove a priori energy estimates locally in time for solutions at the quasilinear regularity threshold under irrotationality and subcriticality assumptions. We use the weak dissipativity of the system, second order Alinhac good unknowns associated with a regularizing diﬀeomorphism, and a new type of hidden boundary regularity.

Source: Journal de l’École polytechnique — Mathématiques

DOI: 10.5802/jep.325

Authors: Tatsuo Iguchi, David Lannes

Institutions: Keio University, Centre National de la Recherche Scientifique, Université de Bordeaux, Institut de Mathématiques de Bordeaux

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Agence Nationale de la Recherche

Awards: Avancées fondamentales pour la modélisation des processus clés pour la réduction des impacts des changements climatiques, Boundaries, Congestion and Vorticity in Fluids: A connection with environmental issues