On partial regularity for weak solutions to the Navier-Stokes equations
type: Item
instance of: scholarly article
title: On partial regularity for weak solutions to the Navier-Stokes equations
zbMATH Open document ID: 1062.35065
author: Cheng He
published in: Journal of Functional Analysis
publication date: 2004-08-06T00:00:00Z
review text: The main goal of this paper is to study the partial regularity for general weak solutions to the Navier-Stokes equations, including the Leray-Hopf weak solution. The author shows that \({\mathcal H}^1(S)= 0\) remains valid for a more general weak solution \(u\) in \(L^\infty((0,T), L^2(\Omega))\cap L^2((0,T), H^1_0(\Omega))\), where \(S\) is the set of possible space-time singular points, \({\mathcal H}^\alpha\) is the \(\alpha\)-dimensional Hausdorff measure. Thus he extends a result of Caffarelli, Kohn and Nirenberg to the general weak solution \(u\).
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D03
Mathematics Subject Classification ID: 35D10
zbMATH DE Number: 2083556
zbMATH Keywords: Leray-Hopf weak solution
zbMATH Keywords: space-time singular points
zbMATH Keywords: Hausdorff measure
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: j.jfa.2003.06.009
OpenAlex ID: W2082716250
cites work: Partial regularity of suitable weak solutions of the navier-stokes equations
cites work: Q4040820
cites work: Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations
cites work: Solutions for semilinear parabolic equations in \(L^ p\) and regularity of weak solutions of the Navier-Stokes system
cites work: Boundedness for large \(| x|\) of suitable weak solutions of the Navier-Stokes equations with prescribed velocity at infinity
cites work: Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Erhard Schmidt zu seinem 75. Geburtstag gewidmet
cites work: Removable singularities of weak solutions to the navier-stokes equations
cites work: A new proof of the Caffarelli-Kohn-Nirenberg theorem
cites work: Partial regularity of a generalized solution to the Navier-Stokes equations in exterior domain
cites work: Turbulence and Navier Stokes equations. Proceedings of the conference, held at the University of Paris-Sud, Orsay, June 12-13, 1975
cites work: Partial regularity of solutions to the Navier-Stokes equations
cites work: Hausdorff measure and the Navier-Stokes equations
cites work: Q4730188
cites work: On partial regularity results for the navier-stokes equations
cites work: On interior regularity criteria for weak solutions of the Navier-Stokes equations
cites work: Gradient estimation on Navier-Stokes equations
DOI: 10.1016/J.JFA.2003.06.009
description: scientific article; zbMATH DE number 2083556