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

Xuan Xuan Xi, Yong Zhou, Mimi Hou

• 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.