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

Paicu, Marius ; Zhang, Ping

Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015), p. 813-832 / Harvested from Numdam

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+{\epsilon }^{\sigma }{a}_{0}({x}_{h},\epsilon {x}_{3}),(\epsilon {u}_{0}^{h}({x}_{h},\epsilon {x}_{3}),{u}_{0}^{3}({x}_{h},\epsilon {x}_{3})))$ for some $ \sigma >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.

Détail

Publié le : 2015-01-01

MR 3390085 | Zbl 1326.35247

DOI : https://doi.org/10.1016/j.anihpc.2014.03.006
Classification:  35Q30,  76D03

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