Smooth solutions of the vector Burgers equation in nonsmooth domains
type: Item
instance of: scholarly article
title: Smooth solutions of the vector Burgers equation in nonsmooth domains
zbMATH Open document ID: 0891.35136
published in: Differential and Integral Equations
publication date: 1998-05-17T00:00:00Z
review text: For the equation \(u_t + u \cdot \nabla u = \Delta u\) in dimensions two and three, the initial boundary value problem \(u{|}_{x \in \partial \Omega } = 0\), \(u{|}_{t = 0} = 0\) is considered for an arbitrary open domain \(\Omega \), possibly nonsmooth. Using domain-independent elliptic inequalities of \textit{Xie} [Indiana Univ. Math. J. 40, No. 4, 1185-1192 (1991; Zbl 0736.35012)], existence and uniqueness of smooth solutions on nonsmooth domains is established in a way which is assumed to be eventually transferable to the Navier-Stokes equation.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35D10
Mathematics Subject Classification ID: 35Q30
zbMATH DE Number: 1153442
zbMATH Keywords: elliptic inequalities
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
author: John G. Heywood
author: Wenzheng Xie
reviewed by: Michal Marvan
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1153442