Globally Well-Posedness Results of the Fractional Navier–Stokes Equations on the Heisenberg Group

• Xiaolin Liu ^[1] ; Yong Zhou ^[2]
  1. [1] Macau University of Science and Technology

     Macau University of Science and Technology

     RAE de Macao (China)

     
  2. [2] Xiangtan University

     Xiangtan University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 2, 2024
• Idioma: inglés
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• Resumen

  • In this paper, we investigate the existence and uniqueness of mild solutions to the fractional Navier–Stokes equations related to time derivative of order α ∈ (0, 1). And the mild solution is associated with the sublaplacian provided by the left invariant vector fields on the Heisenberg group.We demonstrate that when the nonlinear external force term matches the applicable conditions, the global mild solution can be obtained by using improved Ascoli–Arzela theorem and Schaefer’s fixed point theorem.