On the Global Existence for the Axisymmetric Euler-Boussinesq System in Critical Besov Spaces

摘要

This paper is devoted to the global existence and uniqueness results for thethree-dimensional Boussinesq system with axisymmetric initial data$v^{0}{\in}B_{2,1}^{5/2}(\RR^3)$ and$ ${\rho}^{0}{\in}B_{2,1}^{1/2}(\RR^3)\capL^{p}(\RR^3)$ with $p>6.$ This system couples the incompressible Eulerequations with a transport-diffusion equation governing the density. In thiscase the Beale-Kato-Majda criterion is not known to be valid and to circumventthis difficulty we use in a crucial way some geometric properties of thevorticity.