Regularity criteria in terms of pressure for the 3-D Navier-Stokes equations in a generic domain
type: Item
instance of: scholarly article
title: Regularity criteria in terms of pressure for the 3-D Navier-Stokes equations in a generic domain
zbMATH Open document ID: 1054.35062
author: Yong Zhou
published in: Mathematische Annalen
publication date: 2004-03-07T00:00:00Z
review text: The initial boundary value problem is considered in \(\Omega\times(0,T)\) \[ \begin{aligned} &\frac{\partial v}{\partial t}-\Delta v+ (v\cdot\nabla )v +\nabla p=0,\quad \nabla\cdot v=0\;\;\text{in\;} \Omega\times(0,T)\\ &v=0 \quad \text{on\;}\partial\Omega\times(0,T)\\ &v(x,0)=0\quad \text{in\;} \Omega.\end{aligned} \] Here \(\Omega\subset \mathbb{R}^3\) is the half-space \(\mathbb{R}^3_+\)or a bounded domain with smooth boundary, or an exterior domain with smooth boundary. It is proved that if \(v(x,t)\) is a Leray-Hopf weak solution of the problem and \(p(x,t)\) or \(\nabla p(x,t)\) satisfies to certain conditions of integrability then \(v(x,t)\) is a smooth solution in \((0,T)\).
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 76D03
zbMATH DE Number: 2051445
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: regularity criterion
zbMATH Keywords: integrability of pressure
reviewed by: Il'ya Sh. Mogilevskii
MaRDI profile type: Publication
full work available at URL: s00208-003-0478-x
OpenAlex ID: W2044532587
DOI: 10.1007/S00208-003-0478-X
description: scientific article; zbMATH DE number 2051445