The Ricci flow is an important tool in geometry, and a main
problem is to understand the stability of fixed points of the flow and the
convergence of solutions to those fixed points. There are many approaches
to this, but one involves maximal regularity theory and a theorem of
Simonett. I will describe this technique and its application to certain
extended Ricci flow systems. These systems arise from manifolds with
extra structure, such as fibration or warped product structures, or Lie
group structures.