Normal solutions to boundary value problems for stationary systems of the Navier-Stokes type
type: Item
instance of: scholarly article
title: Normal solutions to boundary value problems for stationary systems of the Navier-Stokes type
zbMATH Open document ID: 0854.35083
DOI: 10.1007/BF02107339
published in: Siberian Mathematical Journal
publication date: 1996-09-03T00:00:00Z
review text: In the present article, we consider equations with quadratic nonlinearity in a Hilbert space which describe boundary value problems for stationary Navier-Stokes equations for a viscous incompressible fluid. The problem of finding a normal solution can be interpreted from a physical viewpoint, for instance, as the problem of finding a flow with the least vorticity. From a mathematical viewpoint, the posed problem represents an extremal problem for a nonlinear equation in a Hilbert space and its study is carried out by means of control theory for singular distributed systems. The main goal of the article is to construct and justify necessary optimality conditions for a solution and also, on using these conditions, to obtain extremal principles like the Pontryagin maximum principle. Moreover, for the so-called slow normal solutions to a nonlinear equation, a uniqueness theorem is obtained and a variational inequality is derived which is equivalent to the extremal problem in question.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 35B50
zbMATH DE Number: 923550
zbMATH Keywords: stationary Navier-Stokes equations
zbMATH Keywords: normal solution
zbMATH Keywords: necessary optimality conditions for a solution
zbMATH Keywords: extremal principles
zbMATH Keywords: slow normal solutions
zbMATH Keywords: uniqueness
zbMATH Keywords: variational inequality
author: A. Yu. Chebotarev
MaRDI profile type: Publication
cites work: Q3935753
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full work available at URL: https://doi.org/10.1007/bf02107339
OpenAlex ID: W2096897909
description: scientific article; zbMATH DE number 923550