Global well-posedness of the three dimensional incompressible anisotropic Navier–Stokes system. (December 2016)

• Record Type: Journal Article
• Authors: Yan, Kai; Yin, Zhaoyang
• Is Part Of: Nonlinear analysis. Volume 32(2016)
• Page Start: 52
• Page End: 73
• Publication Date: 2016-12
• Subjects: Anisotropic Navier–Stokes system -- Global well-posedness -- Besov–Sobolev spaces; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.03.015
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we study the global well-posed problem for the three dimensional incompressible anisotropic Navier–Stokes system (ANS) with initial data in the scaling invariant Besov–Sobolev type spaces. We prove that (ANS) has a unique global solution provided that the initial vertical velocity is large while initial horizontal data are sufficiently small compared with the horizontal viscosity. In particular, our result implies the global well-posedness of (ANS) with highly oscillating initial data.