On the origination of auto-oscillations in flows
type: Item
instance of: scholarly article
title: On the origination of auto-oscillations in flows
zbMATH Open document ID: 0857.34064
DOI: 10.1007/BF02104720
author: L. I. Sazonov
published in: Siberian Mathematical Journal
publication date: 1997-03-17T00:00:00Z
review text: In studying the origination of cycles in nonlinear differential equations of the form \(\omega(dv/dt)+Av= K(v,\delta)\) in Banach spaces one assumed that the operator \(A\) has a bounded inverse. At the same time, in certain problems (parabolic equations in unbounded domains, the flow problem for the Navier-Stokes system) the point \(\lambda=0\) is at least a point of the continuous spectrum of the operator \(A\). We establish that the methods of the article [\textit{V. I. Yudovich}, J. Appl. Math. Mech. 35, 587-603 (1971); translation from Priklad. Math. Mekh. 35, 638-655 (1971; Zbl 0247.76044)] can be transferred to this critical case as well as under a certain subordination of nonlinearity to the operator \(A\). Furthermore, we apply the proposed scheme to the Navier-Stokes system in an exterior domain. In particular, the scheme covers the flow problem which was investigated by other methods in [\textit{K. I. Babenko}, Sov. Math. Dokl. 25, 211-216 (1982); translation from Dokl. Akad. Nauk SSSR 262, 1293-1298 (1982; Zbl 0504.76049)].
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 35Q30
zbMATH DE Number: 917142
zbMATH Keywords: origination of cycles
zbMATH Keywords: Banach spaces
zbMATH Keywords: Navier-Stokes system in an exterior domain
zbMATH Keywords: flow problem
MaRDI profile type: Publication
cites work: Q3800606
cites work: Q5531981
cites work: Q5522633
cites work: Q3216305
cites work: On the smoothness of weak solutions of quasilinear equations in several variables and of variational problems
description: scientific article; zbMATH DE number 917142