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An insight on the fractal power law flow: from a Hausdorff vector calculus perspective

General Mathematics 2022-06-01 v1

Abstract

In the article we suggest the Hausdorff vector calculus based on the Chen Hausdorff calculus for the first time. The Gauss-Ostrogradsky-like, Stokes-like, and Green-like theorems, and Green-like identities are obtained in the framework of the Hausdorff vector calculus. The formula is proposed as a mathematical tool to describe the real world problems for the fractal power-law flow equations with the anomalous diffusion equation. A conjecture for the fractal power-law flow equations analogous to the Smales 15th Problem (one of the Millennium Prize Problems for the Navier--Stokes equations) is also addressed.

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Cite

@article{arxiv.2111.04463,
  title  = {An insight on the fractal power law flow: from a Hausdorff vector calculus perspective},
  author = {Xiao-Jun Yang},
  journal= {arXiv preprint arXiv:2111.04463},
  year   = {2022}
}

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24 pages