An anisotropic Sobolev–Hardy inequality with application to 3D axisymmetric Navier–Stokes equations. Issue 2 (25th January 2020)

• Record Type: Journal Article
• Authors: Yu, Huan
• Is Part Of: Applicable analysis. Volume 99:Issue 2(2020)
• Page Start: 313
• Page End: 325
• Publication Date: 2020-01-25
• Subjects: Navier–Stokes equations -- maximal functions -- anisotropic Sobolev–Hardy inequality; 35Q30 -- 42B25 -- 46E99; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1495326
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we first establish a new anisotropic Sobolev–Hardy inequality in which anisotropic singular weights are permitted. As an application, we study the three-dimensional axisymmetric Navier–Stokes system with non-zero swirl and obtain the global well-posedness result if the angular velocity u θ satisfies sup 0 < t < T ∥ z u θ ( ⋅, t ) ∥ L ∞ ( r ≤ r 0 ) ≤ ϵ, r 0 ∈ ( 0, 1 2 ) .