A remark on the existence proof of Hopf's solution of the Navier-Stokes equation
type: Item
instance of: scholarly article
title: A remark on the existence proof of Hopf's solution of the Navier-Stokes equation
zbMATH Open document ID: 0623.35051
DOI: 10.1007/BF01191364
published in: Archiv der Mathematik
publication date: 1986-01-01T00:00:00Z
review text: The existence of weak solutions of the initial-boundary value problem for Navier-Stokes equation in the desired generality was first shown by E. Hopf in 1950. Lateron \textit{J. L. Lions} gave a different proof within the framework of modern functional analysis [cf. C. R. Acad. Sci. Paris, Sér. I 252, 657-659 (1961; Zbl 0097.104)]. The purpose of this note is to point out that Lions' proof can be simplified using a compactness result of \textit{V. Mustonen} and the author [cf. Ark. Mat. 25, 29-40 (1987)].
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35D05
zbMATH DE Number: 4011061
zbMATH Keywords: existence
zbMATH Keywords: weak solutions
zbMATH Keywords: initial-boundary value problem
zbMATH Keywords: Navier-Stokes equation
zbMATH Keywords: compactness
author: Ruediger Landes
MaRDI profile type: Publication
cites work: Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Erhard Schmidt zu seinem 75. Geburtstag gewidmet
cites work: A strongly nonlinear parabolic initial boundary value problem
cites work: Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l'hydrodynamique
cites work: Q3276102
full work available at URL: https://doi.org/10.1007/bf01191364
OpenAlex ID: W2039012053
description: scientific article; zbMATH DE number 4011061