ON THE GLOBAL WELL-POSEDNESS OF THEAXISYMMETRIC VISCOUS BOUSSINESQ SYSTEM INCRITICAL LEBESGUE SPACES - Hanachi, Adalet; HOUAMED, HAROUNE; Zerguine, Mohamed (DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2020)
The contribution of this paper will be focused on the global existence and uniqueness topic in three-dimensional case of the axisymmetric viscous Boussinesq system in critical Lebesgue spaces. We aim at deriving analogous results for the classical two-dimensional and three-dimensional axisymmetric Navier-Stokes equations recently obtained in [19, 20]. Roughly speaking, we show essentially that if the initial data (v0; ρ0) is axisymmetric and (!0; ρ0) belongs to the critical space L1(Ω) ×L1(R3), with !0 is the initial vorticity associated to v0 and Ω = f(r; z) 2 R2 : r > 0g, then the viscous Boussinesq system has a unique global solution.