JournalsrmiVol. 15, No. 1pp. 1–36

The resolution of the Navier-Stokes equations in anisotropic spaces

  • Dragoș Iftimie

    Université de Rennes I, France
The resolution of the Navier-Stokes equations in anisotropic spaces cover
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Abstract

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 HδiH^{\delta_i} in the i-th direction, δ1+δ2+δ3=1/2,1/2<δi<1/2\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 HH and BB denote the usual homogeneous Sobolev and Besov spaces.

Cite this article

Dragoș Iftimie, The resolution of the Navier-Stokes equations in anisotropic spaces. Rev. Mat. Iberoam. 15 (1999), no. 1, pp. 1–36

DOI 10.4171/RMI/248