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

Article type: Research Article

Authors: Sulaiman, Samira

Affiliations: IRMAR, Université de Rennes 1, Campus de Beaulieu, 35 042 Rennes cedex, France. E-mail: samira.sulaiman@univ-rennes1.fr

Abstract: This paper is devoted to the global existence and uniqueness results for the three-dimensional Boussinesq system with axisymmetric initial data v0∈B5/22,1(R3) and ρ0∈B1/22,1(R3)∩Lp(R3) 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.

Keywords: axisymmetric flows, critical Besov spaces, global well-posedness

DOI: 10.3233/ASY-2011-1074

Journal: Asymptotic Analysis, vol. 77, no. 1-2, pp. 89-121, 2012