Tohoku Mathematical Journal

The limiting uniqueness criterion by vorticity for Navier-Stokes equations in Besov spaces

Takayoshi Ogawa and Yasushi Taniuchi

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We investigate a limiting uniqueness criterion in terms of the vorticity for the Navier-Stokes equations in the Besov space. We prove that Leray-Hopf's weak solution is unique under an auxiliary assumption that the vorticity belongs to a scale characterized by the Besov space in space, and the Orlicz space in time direction. As a corollary, we give also the uniqueness criterion in terms of bounded mean oscillation (BMO).

Article information

Tohoku Math. J. (2), Volume 56, Number 1 (2004), 65-77.

First available in Project Euclid: 11 April 2005

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Zentralblatt MATH identifier

Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10]
Secondary: 76D03: Existence, uniqueness, and regularity theory [See also 35Q30] 76D05: Navier-Stokes equations [See also 35Q30]

Besov spaces energy inequality and uniqueness


Ogawa, Takayoshi; Taniuchi, Yasushi. The limiting uniqueness criterion by vorticity for Navier-Stokes equations in Besov spaces. Tohoku Math. J. (2) 56 (2004), no. 1, 65--77. doi:10.2748/tmj/1113246381.

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