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).
Publié le : 2004-03-14
Classification:
Besov spaces,
energy inequality and uniqueness,
35Q30,
76D03,
76D05
@article{1113246381,
author = {Ogawa, Takayoshi and Taniuchi, Yasushi},
title = {The limiting uniqueness criterion by vorticity for Navier-Stokes equations in Besov spaces},
journal = {Tohoku Math. J. (2)},
volume = {56},
number = {1},
year = {2004},
pages = { 65-77},
language = {en},
url = {http://dml.mathdoc.fr/item/1113246381}
}
Ogawa, Takayoshi; Taniuchi, Yasushi. The limiting uniqueness criterion by vorticity for Navier-Stokes equations in Besov spaces. Tohoku Math. J. (2), Tome 56 (2004) no. 1, pp. 65-77. http://gdmltest.u-ga.fr/item/1113246381/