Citation:
Hanachi A, Houamed H, Zerguine M. ON THE GLOBAL WELL-POSEDNESS OF THEAXISYMMETRIC VISCOUS BOUSSINESQ SYSTEM INCRITICAL LEBESGUE SPACES. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS [Internet]. 2020;40 (11) :6473-6506.
Abstract:
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 axisymmetricand (!0; ρ0) belongs to the critical space L1(Ω) ×L1(R3), with !0 is the initialvorticity associated to v0 and Ω = f(r; z) 2 R2 : r > 0g, then the viscousBoussinesq system has a unique global solution.