Existence of Global and Local Mild Solution for the Fractional Navier–Stokes Equations

Awadalla M., Hussain A., Hafeez F., Abuasbeh K.

Symmetry, vol.15, no.2, 2023 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.3390/sym15020343
  • Journal Name: Symmetry
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: Caputo fractional derivatives, mild solutions, Navier–Stokes equations, regularity
  • Uşak University Affiliated: No

Abstract

Navier–Stokes equations (NS-equations) are applied extensively for the study of various waves phenomena where the symmetries are involved. In this paper, we discuss the NS-equations with the time-fractional derivative of order (Formula presented.). In fractional media, these equations can be utilized to recreate anomalous diffusion equations which can be used to construct symmetries. We examine the initial value problem involving the symmetric Stokes operator and gravitational force utilizing the Caputo fractional derivative. Additionally, we demonstrate the global and local mild solutions in (Formula presented.). We also demonstrate the regularity of classical solutions in such circumstances. An example is presented to demonstrate the reliability of our findings.