Revista Matemática Iberoamericana


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Volume 15, Issue 1, 1999, pp. 1–36
DOI: 10.4171/RMI/248

Published online: 1999-04-30

The resolution of the Navier-Stokes equations in anisotropic spaces

Dragoș Iftimie[1]

(1) Université de Rennes I, France

In this paper we prove global existence and uniqueness for solutions of the dimensional Navier-Stokes equations with small initial data in spaces which are $H^{\delta_i}$ in the i-th direction, $\delta_1 + \delta_2 + \delta_3 = 1/2, –1/2 < \delta_i < 1/2$ and in a space which is $L^2$ in the first two directions and B^{1/2}_{2,1} in the third direction where $H$ and $B$ denote the usual homogeneous Sobolev and Besov spaces.

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Iftimie Dragoș: The resolution of the Navier-Stokes equations in anisotropic spaces. Rev. Mat. Iberoam. 15 (1999), 1-36. doi: 10.4171/RMI/248