4.5 Article

Remarks on sparseness and regularity of Navier-Stokes solutions

期刊

NONLINEARITY
卷 35, 期 6, 页码 2858-2877

出版社

IOP Publishing Ltd
DOI: 10.1088/1361-6544/ac62de

关键词

Navier-Stokes equations; regularity theory; sparseness

资金

  1. NSF Postdoctoral Fellowship [2002023]
  2. Simons Foundation [635438]
  3. Division Of Mathematical Sciences
  4. Direct For Mathematical & Physical Scien [2002023] Funding Source: National Science Foundation

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The goal of this paper is to provide a simple proof that sufficiently sparse Navier-Stokes solutions do not develop singularities and to analyze the prior estimates on the sparseness of the vorticity and higher velocity derivatives.
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.

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