Boundedness for large \(| x|\) of suitable weak solutions of the Navier-Stokes equations with prescribed velocity at infinity
type: Item
instance of: scholarly article
title: Boundedness for large \(| x|\) of suitable weak solutions of the Navier-Stokes equations with prescribed velocity at infinity
zbMATH Open document ID: 0777.35056
DOI: 10.1007/BF02097028
published in: Communications in Mathematical Physics
publication date: 1993-05-16T00:00:00Z
review text: The author investigates the boundedness of weak solutions to the Navier- Stokes equations in exterior domains; the result refers to solutions which are perturbations of PR-solutions, a class of stationary flows introduced by R. Finn, which describe the fluid past a body that moves with constant velocity \(v_ \infty\neq 0\). Known results refer to the case \(v_ \infty=0\) or require the PR-solution to be small. The core of the proof consists of an extension of a criterion originally due to Caffarelli, Kohn and Nirenberg, which allows to infer boundedness from a growth property of an integral norm over parabolic cylinders.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 169099
zbMATH Keywords: Navier-Stokes equations in exterior domains
zbMATH Keywords: perturbations of PR- solutions
author: Hans-Christoph Grunau
reviewed by: Josef Bemelmans
MaRDI profile type: Publication
cites work: Partial regularity of suitable weak solutions of the navier-stokes equations
cites work: On the exterior stationary problem for the Navier-Stokes equations, and associated perturbation problems
cites work: Partial regularity of a generalized solution to the Navier-Stokes equations in exterior domain
cites work: On the stability of incompressible viscous fluid motions past objects
cites work: On energy inequality, smoothness and large time behavior in L 2 for weak solutions of the Navier-Stokes equations in exterior domains
cites work: Q4730188
Recommended article: Q4376400
Recommended article: Q4343521
Recommended article: Q3096687
Recommended article: On the boundary regularity of suitable weak solutions to the Navier-Stokes equations
Recommended article: Q3118892
Recommended article: On partial regularity of suitable weak solutions to the Navier-Stokes equations in unbounded domains
Recommended article: Very weak solutions to the Navier-Stokes system in general unbounded domains
Recommended article: Boundary regularity of suitable weak solution for the Navier-Stokes equations
Recommended article: On the uniqueness of bounded very weak solutions to the Navier–Stokes Cauchy problem
Recommended article: Regularity of weak solutions for the Navier-Stokes equations in the class \(L^\infty \)(BMO\(^{-1}\))
description: scientific article; zbMATH DE number 169099