A priori estimates for water waves with emerging bottom

Abstract

We study the beach problem for water waves. The case we consider is a compact fluid domain, where the free surface intersect the bottom along an edge, with a non-zero contact angle. Using elliptic estimates in domain with edges and a new equation on the Taylor coefficient, we establish a priori estimates, for angles smaller than a dimensional constant. Local existence will be derived in a following paper.

Cited by in corpus (1)

• A priori estimates for the 3D compressible free-boundary Euler equations with surface tension in the case of a liquid