  In this paper, we investigate the mean curvature flows for an equifocal
submanifold in a symmetric space of compact type and its focal submanifolds as
initial data. It is known that equifocal submanifolds of codimension greater
than one in irreducible symmetric spaces of compact type occur as principal
orbits of Hermann actions. However, we investigate the flows conceptionally
without use of this fact. Concretely the investigation is performed by
investigating the mean curvature flows having the lifts of the submanifolds to
an (infinite deiminsional separable) Hilbert space through a Riemannian
submersion as initial data.
