Droplet spreading under weak slippage: The optimal asymptotic propagation rate in the multi-dimensional case.
type: Item
instance of: scholarly article
title: Droplet spreading under weak slippage: The optimal asymptotic propagation rate in the multi-dimensional case.
zbMATH Open document ID: 1056.35072
DOI: 10.4171/IFB/63
author: Günther Grün
published in: Interfaces and Free Boundaries
publication date: 2002-01-01T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_abstract.php
review text: Summary: We prove optimal estimates on the growth rate of the support of solutions to the thin-film equation \(u_t+\text{div}(|u|^n \nabla\Delta u)=0\) in space dimensions \(N=2\) and \(N=3\) for parameters \(n\in[2,3)\) which correspond to Navier's slip condition \((n=2)\) or certain variants modeling weaker slippage effects. Our approach relies on a new class of weighted energy estiates. It is inspired by the one-dimensional technique of \textit{J. Hulshof} and \textit{A. E. Shishkov}, [Adv. Differ. Equ. 3, No. 5, 625--642 (1998; Zbl 0953.35072)], and it simplifies their method, mainly with respect to basic integral estimates to be used.
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 1791242
zbMATH Keywords: optimal estimates of the support
zbMATH Keywords: Navier's slip condition
zbMATH Keywords: weighted energy estiates
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1791242