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Zbl 1185.35160
Chen, Qionglei; Zhang, Zhifei
Space-time estimates in the Besov spaces and the Navier-Stokes equations. (English)
[J] Methods Appl. Anal. 13, No. 1, 107-122 (2006). ISSN 1073-2772

The authors prove the title estimates in $\bbfR^n$, $n\ge 3$. These estimates allow the authors to sharpen a regularity criterion for weak solution and the blow-up criterion for smooth solutions of Navier-Stokes equations. Instead of the logarithmic Sobolev inequality, the authors use the frequency localization, the Littlewood-Paley trichotomy decomposition and some commutator estimates.
[Oleg Titow (Berlin)]

MSC 2000:: *35Q30 Stokes and Navier-Stokes equations
76D03 Existence, uniqueness, and regularity theory

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Zentralblatt MATH Berlin [Germany]