## Methods and Applications of Analysis

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

#### 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.

#### Article information

Source
Methods Appl. Anal., Volume 13, Number 1 (2006), 107-122.

Dates
First available in Project Euclid: 5 April 2007