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Space-time estimates in the Besov spaces and the Navier-Stokes equations. (English) Zbl 1185.35160
The authors prove the title estimates in n , n3. 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.
MSC:
35Q30Stokes and Navier-Stokes equations
76D03Existence, uniqueness, and regularity theory