Geodesic
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

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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
Keywords: Inhomogeneous Navier–Stokes equations, Littlewood–Paley theory, Wellposedness 
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     title = {On some large global solutions to {3-D} density-dependent {Navier{\textendash}Stokes} system with slow variable: {Well-prepared} data},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
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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

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