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

DOI: http://dx.doi.org/10.4310/MAA.2006.v13.n1.a6

Authors

Qionglei Chen

Zhifei Zhang

Abstract

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.

Keywords

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

2010 Mathematics Subject Classification

35Q30, 76D03, 76D05

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