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 Hd, of the time-fractional Navier–Stokes system with time derivative of order α∈ (0 , 1). The proof relies on Schaefer’s fixed point theorem. © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.