Axisymmetric solutions of the Navier-Stokes equations

We study the tridimensional Navier-Stokes equations, written in a domain which is invariant under rotation around the vertical axis, or in the whole space R-3; the solutions seeked are also invariant by that rotation, and we look for conditions on the initial data which are close to the natural assumptions in the case of two space dimensions. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.