On some large global solutions to 3-D density-dependent Navier–Stokes system with slow variable: Well-prepared data

Paicu, Marius; Zhang, Ping

doi:10.1016/j.anihpc.2014.03.006

Paicu, Marius ; Zhang, Ping

Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 4, pp. 813-832.

Résumé

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 $(1 + ϵ^{σ} a_{0} (x_{h}, ϵ x_{3}), (ϵ u_{0}^{h} (x_{h}, ϵ x_{3}), u_{0}^{3} (x_{h}, ϵ x_{3})))$ 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.

MR Zbl

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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     author = {Paicu, Marius and Zhang, Ping},
     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},
     pages = {813--832},
     publisher = {Elsevier},
     volume = {32},
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     year = {2015},
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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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