Well-Posedness of Mild Solutions for the Fractional Navier–Stokes Equations in Besov Spaces

• Xuan-Xuan Xi ^[1] ; Yong Zhou ^[2] ; Mimi Hou ^[3]
  1. [1] Xiangtan University

     Xiangtan University

     China

     
  2. [2] Macau University of Science and Technology

     Macau University of Science and Technology

     RAE de Macao (China)

     
  3. [3] Huaibei Normal University

     Huaibei Normal University

     China

     

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 1, 2024
• Idioma: inglés
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• Resumen

  • This paper addresses the existence and uniqueness of mild solution for fractional Navier–Stokes equation in the homogeneous Besov spaces. The existence and uniqueness of the global mild solution with small initial data is established. The results on existence and uniqueness of the local mild solution for arbitrary initial data are also studied. Meanwhile, we obtain properties about the regularity and decay of mild solutions. These conclusions are mainly based on the fixed point theorems, the implicit function theorem on Banach spaces and the properties of Mittag–Leffler functions.

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