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

In this paper, we investigate the existence and uniqueness of mild solutions to the fractional Navier–Stokes equations related to time derivative of order \(\alpha \in (0,1)\). 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.