Résultats de régularité de solutions axisymétriques pour le système de Navier-Stokes

In the first part of the paper, we prove the existence of a unique global solution to the axisymmetric Navier-Stokes system with initial data and external force with . This improves the result obtained by S. Leonardi, J. Málek, J. Necǎs and M. Pokorný S. Leonardi, J. Málek, J. Necǎs, M. Pokorný, On axially symmetric flows in R³, Zeitschrift für analysis und ihre anwendungen, J. Anal. Appl. 18 (3) (1999) 639-649], where H²(R³) regularity was required. In the second part, we state global existence and uniqueness for the axisymmetric Navier-Stokes system with initial data in W2,p(R³) and external force in with 1<p<2. This also improves S. Leonardi, J. Málek, J. Necǎs, M. Pokorný, On axially symmetric flows in R³, Zeitschrift für analysis und ihre anwendungen, J. Anal. Appl. 18 (3) (1999) 639-649] because less integrability is required on v₀ and on f.