Backward uniqueness and unique continuation for solutions to the Navier- Stokes equations on an exterior domain
type: Item
instance of: scholarly article
title: Backward uniqueness and unique continuation for solutions to the Navier- Stokes equations on an exterior domain
zbMATH Open document ID: 0546.76038
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 1983-01-01T00:00:00Z
review text: Using the results obtained by \textit{J. Serrin} [Nonlinear Prob., Proc. Sympos. Madison, 69-98 (1963; Zbl 0115.085)], \textit{D. E. Edmunds} [Arch. Ration. Mech. Anal. 14, 171-176 (1963; Zbl 0126.423)], \textit{S. Rionero} and \textit{G. P. Galdi} [Arch. Ration. Mech. Anal. 62, 295-301 (1976; Zbl 0351.35070)], the author shows the backward uniqueness of the solution of the Navier-Stokes equations on a spatially unbounded domain exterior to a compact set in \({\mathbb{R}}^ 3\). This result is established under weaker decay assumptions than those required in Edmund's analysis. The asymptotic behaviour (the determination of the rate of decay in time) of the same Navier-Stokes equations is also developed.
Mathematics Subject Classification ID: 76D05
zbMATH DE Number: 3870821
zbMATH Keywords: unique continuation
zbMATH Keywords: backward uniqueness
zbMATH Keywords: spatially unbounded domain exterior to a compact set
zbMATH Keywords: decay assumptions
zbMATH Keywords: asymptotic behaviour
author: Brian Straughan
reviewed by: Titus Petrila
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3870821