Weak Solutions to the complex Monge-Ampère flows on compact Kähler manifolds : general measures on the right-hand side

We show the existence of a bounded solution to the Cauchy problem for the complex Monge-Ampère flow on a compact Kähler manifold, with the right-hand side of the form $dt \wedge dμ$ where $dμ$ is either a Monge-Ampère measure with a bounded potential or dominated by a Monge-Ampère measure with a Höl