Methods and Applications of Analysis

Volume 13 (2006)

Number 1

Space-Time Estimates in the Besov Spaces and the Navier-Stokes Equations

Pages: 107 – 122



Qionglei Chen

Zhifei Zhang


In this paper, we establish the space-time estimates in the Besov spaces of the solution to the Navier-Stokes equations in $\bold R^n , n\geq 3$. As an application, we improve some known results about the regularity criterion of weak solutions and the blow-up criterion of smooth solutions. Our main tools are the frequency localization and the Littlewood-Paley decomposition.


Navier-Stokes equations, Besov space, regularity criterion, Littlewood-Paley decomposition

2010 Mathematics Subject Classification

35Q30, 76D03, 76D05

Published 1 January 2006