On the global regularity of axisymmetric Navier-Stokes-Boussinesq system

H. Abidi, 2008, <em>Résultats de régularité de solutions axisymétriques pour le système de Navier-Stokes</em>,, Bull. Sc. Math., 132, 592, 10.1016/j.bulsci.2007.10.001

H. Abidi, 2007, <em>On the global well-posedness for Boussinesq System</em>,, J. Diff. Equa., 233, 199, 10.1016/j.jde.2006.10.008

H. Abidi, 2010, <em>On the global well-posedness for the axisymmetric Euler equations</em>,, Mathematische Annalen, 347, 15, 10.1007/s00208-009-0425-6

H. Abidi, 2007, <em>Existence globale pour un fluide inhomogène</em>,, Annales Inst. Fourier, 57, 883, 10.5802/aif.2280

J. Ben Ameur, 2002, <em>Limite non visqueuse pour les fluides incompressibles axisymétrique</em>,, in, 29

J.-M. Bony, 1981, <em>Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires</em>,, Ann. de l'Ecole Norm. Sup., 14, 209, 10.24033/asens.1404

Y. Brenier, 2009, <em>Optimal transport, convection, magnetic relaxation and generalized Boussinesq equations</em>,, J. Nonlinear Sci., 19, 547, 10.1007/s00332-009-9044-3

D. Chae, 2006, <em>Global regularity for the $2$-D Boussinesq equations with partial viscous terms</em>,, Advances in Math., 203, 497, 10.1016/j.aim.2005.05.001

J.-Y. Chemin, 1998, "Perfect Incompressible Fluids,", Oxford University Press 1998.

J.-Y. Chemin, 2006, <em>On the global wellposedness of the $3$-D incompressible Navier-Stokes equations with large initial data</em>,, Ann. de l'Ecole Norm. Sup., 39, 679, 10.1016/j.ansens.2006.07.002

J.-Y. Chemin, 2009, <em>Wellposedness and stability results for the Navier-Stokes equations in</em> $R^3$,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 26, 599, 10.1016/j.anihpc.2007.05.008

R. Danchin, 2007, <em>Axisymmetric incompressible flows with bounded vorticity</em>,, Russian Math. Surveys, 62, 73, 10.1070/RM2007v062n03ABEH004412

R. Danchin, 2009, <em>Global well-posedness issues for the inviscid Boussinesq system with Yudovich's type data</em>,, Comm. Math. Phys., 290, 1, 10.1007/s00220-009-0821-5

R. Danchin, 2008, <em>Le théorème de Leray et le théorème de Fujita-Kato pour le système de Boussinesq partiellement visqueux</em>,, Bulletin de la S. M. F., 136, 261

R. Danchin, <em>Global existence results for the anistropic Boussinesq system in dimension two</em>,, preprint

T. Hmidi, 2007, <em>On the global well-posedness of the two-dimensional Boussinesq system with a zero diffusivity</em>,, Adv. Differential Equations, 12, 461, 10.57262/ade/1355867459

T. Hmidi, 2009, <em>On the global well-posedness of the Boussinesq system with zero viscosity</em>,, Indiana Univ. Math. J., 58, 1591, 10.1512/iumj.2009.58.3590

T. Hmidi, <em>Global well-posedness for Euler-Boussinesq system</em>,, preprint

T. Hmidi, <em>Global well-posedness for Navier-Stokes-Boussinesq system</em>,, preprint

R. O'Neil, 1963, <em>Convolution operators and L(p,q) spaces</em>,, Duke Math. J., 30, 129, 10.1215/S0012-7094-63-03015-1

O. A. Ladyzhenskaya, 1968, <em>Unique solvability in large of a three-dimensional Cauchy problem for the Navier-Stokes equations in the presence of axial symmetry</em>,, Zapisky Nauchnych Sem. LOMI, 7, 155

P.-G. Lemarié, 2002, "Recent Developments in the Navier-Stokes Problem,", CRC Press, 10.1201/9781420035674

S. Leonardi, 1999, <em>On axially symmetric flows in</em> $\RR^3$,, Zeitschrift für Analysis und ihre Anwendungen [Journal for Analysis and its Applications Volume], 18, 639, 10.4171/ZAA/903

J. Leray, 1934, <em>Sur le mouvement d'un liquide visqueux remplissant l'espace</em>,, Acta mathematica, 63, 193, 10.1007/BF02547354

T. Shirota, 1994, <em>Note on global existence for axially symmetric solutions of the Euler system</em>,, Proc. Japan Acad. Ser. A Math. Sci., 70, 299, 10.3792/pjaa.70.299

M. R. Ukhovskii, 1968, <em>Axially symmetric flows of ideal and viscous fluids filling the whole space</em>,, Prikl. Mat. Meh., 32, 59