We present two characterizations of smooth compact Ricci flow solutions solely in terms of metrics and measures (one of them only works under positive scalar curvature along the flow); thus, provide weak formulations that are generalized to the singular setting in a straightforward manner. These characterizations are achieved by weakly formulating super Ricci flows and imposing a saturation condition (solely in terms of metric and measure) to ensure the super Ricci flow inequality is an equality.
Sajjad Lakzian (Thu,) studied this question.