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An Insight On The Fractal Power Law Flow: From A Hausdorff Vector Calculus Perspective

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  • XIAO-JUN YANG

    (School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China2State Key Laboratory for Geo-Mechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China3Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80257, Jeddah 21589, Saudi Arabia)

Abstract

In the paper, 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 Smale’s 15th problem and one of Millennium Prize Problems for the Navier–Stokes equations is also addressed.

Suggested Citation

  • Xiao-Jun Yang, 2022. "An Insight On The Fractal Power Law Flow: From A Hausdorff Vector Calculus Perspective," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(03), pages 1-13, May.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:03:n:s0218348x22500542
    DOI: 10.1142/S0218348X22500542
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