On the global well-posedness of the Boussinesq system with zero viscosity

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1. H. Abidi, T. Hmidi, On the global well-posedness for Boussinesq system, J. Diff. Equa.,233, 1 (2007) 199-220. Zbl1111.35032MR2290277
2. J.-M. Bony, Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires, Ann. de l’ Ecole Norm. Sup., 14 (1981) 209-246. Zbl0495.35024
3. J. T. Beale, T. Kato, A. Majda, Remarks on the breakdown of smooth solutions for $3$-D Euler equations, Comm. Math. Phys 94 (1984) 61-66. Zbl0573.76029MR763762
4. J. R. Cannon, E. Dibenedetto, The initial value problem for the Boussinesq equations with data in $L^p,$ in Approximation Methods for Navier-Stokes Problems, Lecture Notes in Math. 771, Springer, Berlin 1980, 129-144. Zbl0429.35059MR565993
5. D. Chae, Global regularity for the $2$-D Boussinesq equations with partial viscous terms, Advances in Math., 203, 2 (2006) 497-513. Zbl1100.35084MR2227730
6. J.-Y. Chemin, Perfect incompressible Fluids, Oxford University Press. Zbl0927.76002MR1688875
7. J.-Y. Chemin, Théorèmes d’unicité pour le système de Navier-Stokes tridimensionnel, J. Anal. Math. 77 (1999) 27-50. Zbl0938.35125
8. R. Danchin, M. Paicu, Le théorème de Leray et le théorème de Fujita-Kato pour le système de Boussinesq partiellement visqueux, to appear in Bull. S. M. F. 
9. B. Guo, Spectral method for solving two-dimensional Newoton-Boussinesq equation, Acta Math. Appl. Sinica, 5 (1989) 201-218. Zbl0681.76048MR1013438
10. T. Hmidi, Régularité höldérienne des poches de tourbillon visqueuses, J. Math. Pures Appl. (9) 84, 11 (2005) 1455-1495. Zbl1095.35024MR2181457
11. T. Hmidi, Poches de tourbillon singulières dans un fluide faiblement visqueux. Rev. Mat. Iberoamericana, 22, 2 (2006) 489-543. Zbl1127.35037MR2294788
12. T. Hmidi, S. Keraani, On the global well-posedness of the two-dimensional Boussinesq system with a zero diffusivity, Adv. Diff. Equations, 12, 4 (2007) 461-480. Zbl1154.35073MR2305876
13. T. Hmidi, S. Keraani, Incompressible viscous flows in borderline Besov spaces, to appear in Arch. Ratio. Mech. Ana. Zbl1147.76014
14. T. Y. Hou, C. Li, Global well-posedness of the viscous Boussinesq equations, Discrete and Continuous Dynamical Systems, $\mathbf{12},$ 1 (2005) 1-12. Zbl1274.76185MR2121245
15. O. Sawada, Y. Taniuchi, On the Boussinesq flow with nondecaying initial data, Funkcial. Ekvac. 47, 2 (2004) 225-250. Zbl1118.35037MR2108674
16. M. Vishik, Hydrodynamics in Besov Spaces, Arch. Rational Mech. Anal 145(1998) 197-214. Zbl0926.35123MR1664597