Mathematische Zeitschrift

, Volume 235, Issue 1, pp 173–194 | Cite as

Bilinear estimates in BMO and the Navier-Stokes equations

  • Hideo Kozono
  • Yasushi Taniuchi
Original article


We prove that the BMO norm of the velocity and the vorticity controls the blow-up phenomena of smooth solutions to the Navier-Stokes equations. Our result is applied to the criterion on uniqueness and regularity of weak solutions in the marginal class.

Mathematics Subject Classification (1991): 35Q30 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Hideo Kozono
    • 1
  • Yasushi Taniuchi
    • 2
  1. 1.Mathematical Institute, Tohoku University, Sendai, 980–8578 Japan (e-mail:
  2. 2.Graduate School of Mathematics, Nagoya University, Nagoya, 464–8602 Japan (

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