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Bilinear estimates in BMO and the Navier-Stokes equations

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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.

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Received February 15, 1999; in final form October 11, 1999 / Published online July 3, 2000

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Kozono, H., Taniuchi, Y. Bilinear estimates in BMO and the Navier-Stokes equations. Math Z 235, 173–194 (2000). https://doi.org/10.1007/s002090000130

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  • DOI: https://doi.org/10.1007/s002090000130

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