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

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.

preprint2021arXivOpen access
Xiao-Jun Yang
math.GM
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Xiao-Jun Yang

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