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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Abstract

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

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

Dates
First available in Project Euclid: 11 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1113246381

Digital Object Identifier
doi:10.2748/tmj/1113246381

Mathematical Reviews number (MathSciNet)
MR2028918

Zentralblatt MATH identifier
1083.35096

Subjects
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]

Keywords
Besov spaces energy inequality and uniqueness

Citation

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. https://projecteuclid.org/euclid.tmj/1113246381


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