On the global existence for the axisymmetric Euler-Boussinesq system in critical Besov spaces

Samira Sulaiman (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

This paper is devoted to the global existence and uniqueness results for the three-dimensional Boussinesq system with axisymmetric initial data upsilon(0) is an element of B-2,1(5/2)(R-3) and rho(0) is an element of B-2,1(1/2)(R-3) boolean AND L-p(R-3) with p > 6. This system couples the incompressible Euler equations with a transport-diffusion equation governing the density. In this case the Beale-Kato-Majda criterion (see [2]) is not known to be valid and to circumvent this difficulty we use in a crucial way some geometric properties of the vorticity.

Mots clés: axisymmetric flows; critical Besov spaces; global well-posedness

Domaines: Equations aux dérivées partielles [math.AP]

Samira Sulaiman. On the global existence for the axisymmetric Euler-Boussinesq system in critical Besov spaces. Asymptotic Analysis, 2012, 77 (1-2), pp.89-121. ⟨10.3233/ASY-2011-1074⟩. ⟨hal-00708564⟩