  For some class of geometric flows, we obtain the (logarithmic) Sobolev
inequalities and their equivalence up to different factors directly and also
obtain the long time non-collapsing and non-inflated properties, which
generalize the results in the case of Ricci flow or List-Ricci flow or
harmonic-Ricci flow. As applications, for mean curvature flow in Lorentzian
space with nonnegative sectional curvature and twisted K\"ahler-Ricci flow on
Fano manifolds, we get the results above.
