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, Volume 32 (2015) no. 4, p. 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 : https://doi.org/10.1016/j.anihpc.2014.03.006
Classification:  35Q30,  76D03
Keywords: Inhomogeneous Navier–Stokes equations, Littlewood–Paley theory, Wellposedness
@article{AIHPC_2015__32_4_813_0,
     author = {Paicu, Marius and Zhang, Ping},
     title = {On some large global solutions to 3-D density-dependent Navier--Stokes system with slow variable: Well-prepared data},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {32},
     number = {4},
     year = {2015},
     pages = {813-832},
     doi = {10.1016/j.anihpc.2014.03.006},
     zbl = {1326.35247},
     mrnumber = {3390085},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2015__32_4_813_0}
}
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, Volume 32 (2015) no. 4, pp. 813-832. doi : 10.1016/j.anihpc.2014.03.006. http://www.numdam.org/item/AIHPC_2015__32_4_813_0/

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