  We show that immersed Lagrangian Floer cohomology in compact rational
symplectic manifolds is invariant under Maslov flows such as coupled mean
curvature/Kaehler-Ricci flow in the sense of Smoczyk as a pair of
self-intersection points is born or dies at a self-tangency, using results of
Ekholm-Etnyre-Sullivan. This proves part of a conjecture of Joyce. We give a
lower bound on the time for which the Floer cohomology is invariant under the
(forward or backwards) flow, if it exists.
