On the global well-posedness of the Boussinesq system with zero viscosity
Séminaire Équations aux dérivées partielles (Polytechnique) (2007-2008), Talk no. 24, 15 p.

In this paper we prove the global well-posedness of the two-dimensional Boussinesq system with zero viscosity for rough initial data.

@article{SEDP_2007-2008____A24_0,
     author = {Hmidi, Taoufik},
     title = {On the global well-posedness of the Boussinesq system with zero viscosity},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique)},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2007-2008},
     note = {talk:24},
     mrnumber = {2532956},
     language = {en},
     url = {http://www.numdam.org/item/SEDP_2007-2008____A24_0}
}
Hmidi, Taoufik. On the global well-posedness of the Boussinesq system with zero viscosity. Séminaire Équations aux dérivées partielles (Polytechnique) (2007-2008), Talk no. 24, 15 p. http://www.numdam.org/item/SEDP_2007-2008____A24_0/

[1] H. Abidi, T. Hmidi, On the global well-posedness for Boussinesq system, J. Diff. Equa.,233, 1 (2007) 199-220. | MR 2290277 | Zbl 1111.35032

[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. | Numdam | Zbl 0495.35024

[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. | MR 763762 | Zbl 0573.76029

[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. | MR 565993 | Zbl 0429.35059

[5] D. Chae, Global regularity for the 2-D Boussinesq equations with partial viscous terms, Advances in Math., 203, 2 (2006) 497-513. | MR 2227730 | Zbl 1100.35084

[6] J.-Y. Chemin, Perfect incompressible Fluids, Oxford University Press. | MR 1688875 | Zbl 0927.76002

[7] J.-Y. Chemin, Théorèmes d’unicité pour le système de Navier-Stokes tridimensionnel, J. Anal. Math. 77 (1999) 27-50. | Zbl 0938.35125

[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. | MR 1013438 | Zbl 0681.76048

[10] T. Hmidi, Régularité höldérienne des poches de tourbillon visqueuses, J. Math. Pures Appl. (9) 84, 11 (2005) 1455-1495. | MR 2181457 | Zbl 1095.35024

[11] T. Hmidi, Poches de tourbillon singulières dans un fluide faiblement visqueux. Rev. Mat. Iberoamericana, 22, 2 (2006) 489-543. | MR 2294788 | Zbl 1127.35037

[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. | MR 2305876

[13] T. Hmidi, S. Keraani, Incompressible viscous flows in borderline Besov spaces, to appear in Arch. Ratio. Mech. Ana.

[14] T. Y. Hou, C. Li, Global well-posedness of the viscous Boussinesq equations, Discrete and Continuous Dynamical Systems, 12, 1 (2005) 1-12. | MR 2121245 | Zbl pre02154350

[15] O. Sawada, Y. Taniuchi, On the Boussinesq flow with nondecaying initial data, Funkcial. Ekvac. 47, 2 (2004) 225-250. | MR 2108674 | Zbl 1118.35037

[16] M. Vishik, Hydrodynamics in Besov Spaces, Arch. Rational Mech. Anal 145(1998) 197-214. | MR 1664597 | Zbl 0926.35123