Local and global existence of mild solutions of time-fractional Navier–Stokes system posed on the Heisenberg group

Abstract

This paper is a development of the results and techniques of the two papers (Carvalho-Neto and Planas in J Differ Equ 259:2948–2980, 2015; Oka in J Math Anal Appl 473:382–407, 2019) for the aim of addressing the existence and uniqueness of local and global mild solutions, on the Heisenberg group $$\mathbb {H}^d$$ , of the time-fractional Navier–Stokes system with time derivative of order $$\alpha \in (0, 1)$$ . The proof relies on Schaefer’s fixed point theorem.