Revista Matemática Iberoamericana


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Volume 21, Issue 1, 2005, pp. 179–235
DOI: 10.4171/RMI/420

Published online: 2005-04-30

Équation anisotrope de Navier-Stokes dans des espaces critiques

Marius Paicu[1]

(1) Université Paris-Sud, Orsay, France

We study the tridimensional Navier-Stokes equation when the value of the vertical viscosity is zero, in a critical space (invariant by the scaling). We shall prove local in time existence of the solution, respectively global in time when the initial data is small compared with the horizontal viscosity.

Keywords: Navier-Stokes equation, critical spaces, anisotropic viscosity

Paicu Marius: Équation anisotrope de Navier-Stokes dans des espaces critiques. Rev. Mat. Iberoam. 21 (2005), 179-235. doi: 10.4171/RMI/420