Open Access
April, 2012 Bilinear estimates in dyadic BMO and the Navier-Stokes equations
Eiichi NAKAI, Tsuyoshi YONEDA
J. Math. Soc. Japan 64(2): 399-422 (April, 2012). DOI: 10.2969/jmsj/06420399


We establish bilinear estimates in dyadic BMO as an extension of Kozono and Taniuchi's result on the usual BMO. To establish the bilinear estimates we use sharp maximal functions, while they used the boundedness of pseudo-differential operators by Coifman and Meyer. By this extension we prove that the dyadic BMO norm of the velocity controls the blow-up phenomena of smooth solutions to the Navier-Stokes equations. Moreover, we give an odd function with type II singularity which clarifies the difference between BMO and dyadic BMO.


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Eiichi NAKAI. Tsuyoshi YONEDA. "Bilinear estimates in dyadic BMO and the Navier-Stokes equations." J. Math. Soc. Japan 64 (2) 399 - 422, April, 2012.


Published: April, 2012
First available in Project Euclid: 26 April 2012

zbMATH: 1251.35073
MathSciNet: MR2916074
Digital Object Identifier: 10.2969/jmsj/06420399

Primary: 35Q30 , 46E35
Secondary: 42B35

Keywords: bilinear estimate , bounded mean oscillation , dyadic BMO , Navier-Stokes equation

Rights: Copyright © 2012 Mathematical Society of Japan

Vol.64 • No. 2 • April, 2012
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