<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Hanachi, Adalet</style></author><author><style face="normal" font="default" size="100%">Houamed, Haroune</style></author><author><style face="normal" font="default" size="100%">Zerguine, Mohamed</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON THE GLOBAL WELL-POSEDNESS OF THEAXISYMMETRIC VISCOUS BOUSSINESQ SYSTEM INCRITICAL LEBESGUE SPACES</style></title><secondary-title><style face="normal" font="default" size="100%">DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2020</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">doi:10.3934/dcds.2020287</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">40</style></volume><pages><style face="normal" font="default" size="100%">6473-6506</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">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 &amp;gt; 0g, then the viscousBoussinesq system has a unique global solution.</style></abstract><issue><style face="normal" font="default" size="100%">11</style></issue></record></records></xml>