Tohoku Mathematical Journal
2004

March
SECOND SERIES VOL. 56, NO. 1

Tohoku Math. J.
56 (2004), 65-77

Title THE LIMITING UNIQUENESS CRITERION BY VORTICITY FOR NAVIER-STOKES EQUATIONS IN BESOV SPACE

Author Takayoshi Ogawa and Yasushi Taniuchi

(Received February 12, 2002, revised September 3, 2003)
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).

2000 Mathematics Subject Classification. Primary 35Q30; Secondary 76D05.

Key words and phrases. Besov spaces, energy inequality and uniqueness.

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