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Estimates of Mild Solutions of Navier–Stokes Equations in Weak Herz-Type Besov–Morrey Spaces

Author

Listed:
  • Ruslan Abdulkadirov

    (North-Caucasus Center for Mathematical Research, North-Caucasus Federal University, 355009 Stavropol, Russia)

  • Pavel Lyakhov

    (Department of Automation and Control Processes, Saint Petersburg Electrotechnical University “LETI”, 197376 Saint Petersburg, Russia)

Abstract

The main goal of this article is to provide estimates of mild solutions of Navier–Stokes equations with arbitrary external forces in R n for n ≥ 2 on proposed weak Herz-type Besov–Morrey spaces. These spaces are larger than known Besov–Morrey and Herz spaces considered in known works on Navier–Stokes equations. Morrey–Sobolev and Besov–Morrey spaces based on weak-Herz space denoted as W K ˙ p , q α M μ s and W K ˙ p , q α N ˙ μ , r s , respectively, represent new properties and interpolations. This class of spaces and its developed properties could also be employed to study elliptic, parabolic, and conservation-law type PDEs.

Suggested Citation

  • Ruslan Abdulkadirov & Pavel Lyakhov, 2022. "Estimates of Mild Solutions of Navier–Stokes Equations in Weak Herz-Type Besov–Morrey Spaces," Mathematics, MDPI, vol. 10(5), pages 1-13, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:680-:d:755938
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    Cited by:

    1. Liu, Mingyang & Gao, Guangjun & Khoo, Boo Cheong & He, Zhenhu & Jiang, Chen, 2022. "A cell-based smoothed finite element model for non-Newtonian blood flow," Applied Mathematics and Computation, Elsevier, vol. 435(C).

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