On the stationary and nonstationary Navier-Stokes equations in \(R^ n\)
type: Item
instance of: scholarly article
title: On the stationary and nonstationary Navier-Stokes equations in \(R^ n\)
zbMATH Open document ID: 0682.35089
DOI: 10.1007/BF01762396
author: Paolo Secchi
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1988-01-01T00:00:00Z
review text: The author solves the stationary and nonstationary Navier-Stokes equations: \[ -\nu \Delta v+(v\cdot \nabla)v+\nabla p=f,\quad \nabla \cdot v=0\quad in\quad R^ n,\quad \lim_{| x| \to \infty}v(x)=0,\quad \lim_{| x| \to \infty}p(x)=0 \] and \[ u'- \nu \Delta u+(u\cdot \nabla)u+\nabla q=f,\quad \nabla \cdot u=0\quad in\quad (0,T)\times R^ n, \] \[ u(0,x)=u_ 0(x),\quad \lim_{| x| \to \infty}u(t,x)=0,\quad \lim_{| x| \to \infty}q(t,x)=0. \] The existence and uniqueness results are derived. The asymptotic behaviour of a stationary solution u is established too. The cases \(n\geq 3\), \(n=3\) and \(n\geq 4\) are considered.
reviewed by: Igor Bock
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 4117090
zbMATH Keywords: existence and uniqueness
MaRDI profile type: Publication
cites work: Q3736200
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full work available at URL: https://doi.org/10.1007/bf01762396
OpenAlex ID: W2067825341
description: scientific article; zbMATH DE number 4117090