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Energy methods for fractional Navier–Stokes equations

Author

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  • Zhou, Yong
  • Peng, Li
  • Ahmad, Bashir
  • Alsaedi, Ahmed

Abstract

In this paper we make use of energy methods to study the Navier–Stokes equations with time-fractional derivative. Such equations can be used to simulate anomalous diffusion in fractal media. In the first step, we construct a regularized equation by using a smoothing process to transform unbounded differential operators into bounded operators and then obtain the approximate solutions. The second part describes a procedure to take a limit in the approximation program to present a global solution to the objective equation.

Suggested Citation

  • Zhou, Yong & Peng, Li & Ahmad, Bashir & Alsaedi, Ahmed, 2017. "Energy methods for fractional Navier–Stokes equations," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 78-85.
    • Handle: RePEc:eee:chsofr:v:102:y:2017:i:c:p:78-85
    DOI: 10.1016/j.chaos.2017.03.053
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    Cited by:

    1. Syam, Muhammed I. & Sharadga, Mwaffag & Hashim, I., 2021. "A numerical method for solving fractional delay differential equations based on the operational matrix method," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).

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