On the regularity of solutions  to the Navier-Stokes equations

Vittorino Pata

doi:10.3934/cpaa.2012.11.747

Article Contents

2012, Volume 11, Issue 2: 747-761. Doi: 10.3934/cpaa.2012.11.747

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On the regularity of solutions to the Navier-Stokes equations

Vittorino Pata^1,

1.
Politecnico di Milano - Dipartimento di Matematica "F. Brioschi", Via Bonardi 9, 20133 Milano

Received: October 31, 2010

Revised: March 31, 2011

Published: February 2012

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Abstract

This article is concerned with the incompressible Navier-Stokes equations in a three-dimensional domain. A criterion of Prodi-Serrin type up to the boundary for global existence of strong solutions is established.

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Mathematics Subject Classification: Primary: 35Q30; Secondary: 76D03, 76D05.

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