Generalized solutions of the capillary problem
type: Item
instance of: scholarly article
title: Generalized solutions of the capillary problem
zbMATH Open document ID: 1060.49030
author: Markus Scholz
published in: Journal of Mathematical Fluid Mechanics
publication date: 2004-10-28T00:00:00Z
review text: It is known that the capillary problem has not always a solution if the gravity is zero even for bounded domains with smooth boundaries. In the case that a two-dimensional domain has a cusp with an opening angle zero then there is no solution. The author shows that there exists a generalized solution in the sense of M. Miranda. The major difficulty was that previous existence results are based on the assumption of a Lipschitz boundary which is not the case here. The main tool for the proof of the existence is an existence-nonexistence theorem for generalized solutions due to Finn. The results of the author provide hints where the liquid along small touching tubes is located; see a paper of the same author [J. Math. Fluid Mech. 6, 295--310 (2004; Zbl 1050.92041)].
Mathematics Subject Classification ID: 49Q10
Mathematics Subject Classification ID: 76B45
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 49J27
Mathematics Subject Classification ID: 76M30
zbMATH DE Number: 2111574
zbMATH Keywords: capillary surfaces, zero gravity, cusps
zbMATH Keywords: generalized solutions
reviewed by: Erich Miersemann
MaRDI profile type: Publication
full work available at URL: s00021-003-0094-2
OpenAlex ID: W4213178836
DOI: 10.1007/S00021-003-0094-2
description: scientific article; zbMATH DE number 2111574