Methods and Applications of Analysis

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

Qionglei Chen and Zhifei Zhang

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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

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

First available in Project Euclid: 5 April 2007

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Zentralblatt MATH identifier

Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 35D10 76D03: Existence, uniqueness, and regularity theory [See also 35Q30] 76D05: Navier-Stokes equations [See also 35Q30]

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


Chen, Qionglei; Zhang, Zhifei. Space-Time Estimates in the Besov Spaces and the Navier-Stokes Equations. Methods Appl. Anal. 13 (2006), no. 1, 107--122.

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