On some large global solutions to 3-D density-dependent Navier–Stokes system with slow variable: Well-prepared data
Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 4, pp. 813-832.

In this paper, we consider the global wellposedness of 3-D incompressible inhomogeneous Navier–Stokes equations with initial data slowly varying in the vertical variable, that is, initial data of the form (1+ϵ σ a 0 (x h ,ϵx 3 ),(ϵu 0 h (x h ,ϵx 3 ),u 0 3 (x h ,ϵx 3 ))) for some σ>0 and ε being sufficiently small. We remark that initial data of this type does not satisfy the smallness conditions in [11,18] no matter how small ε is.

DOI : 10.1016/j.anihpc.2014.03.006
Classification : 35Q30, 76D03
Mots-clés : Inhomogeneous Navier–Stokes equations, Littlewood–Paley theory, Wellposedness 
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Paicu, Marius; Zhang, Ping. On some large global solutions to 3-D density-dependent Navier–Stokes system with slow variable: Well-prepared data. Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 4, pp. 813-832. doi : 10.1016/j.anihpc.2014.03.006. http://www.numdam.org/articles/10.1016/j.anihpc.2014.03.006/

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