Remarks on sparseness and regularity of Navier-Stokes solutions

被引:3
作者
Albritton, Dallas [1 ]
Bradshaw, Zachary [2 ]
机构
[1] Inst Adv Study, Sch Math, 1 Einstein Dr, Princeton, NJ 08540 USA
[2] Univ Arkansas, Dept Math, Fayetteville, AR 72701 USA
基金
美国国家科学基金会;
关键词
Navier-Stokes equations; regularity theory; sparseness; SELF-SIMILAR SOLUTIONS; EULER EQUATIONS; SINGULARITY FORMATION; B-INFINITY; INFINITY(-1); DISSIPATION;
D O I
10.1088/1361-6544/ac62de
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The goal of this paper is twofold. First, we give a simple proof that sufficiently sparse Navier-Stokes solutions do not develop singularities. This provides an alternative to the approach of (Grujic 2013 Nonlinearity 26 289-96), which is based on analyticity and the 'harmonic measure maximum principle'. Second, we analyse the claims in (Bradshaw et al 2019 Arch. Ration. Mech. Anal. 231 1983-2005; Grujic and Xu 2019 arXiv:1911.00974) that a priori estimates on the sparseness of the vorticity and higher velocity derivatives reduce the 'scaling gap' in the regularity problem.
引用
收藏
页码:2858 / 2877
页数:20
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