Methods and Applications of Analysis
Volume 13 (2006)
Space-Time Estimates in the Besov Spaces and the Navier-Stokes Equations
Pages: 107 – 122
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