Chen's short-time regularization conjecture for the Calabi flow

Let $(M,\\omega)$ be a closed Kähler manifold and let $u_0$ be a $C^{1,1}$ Kähler potential, so that its complex Hessian is bounded and $\omega_{u_0}=\omega+\sqrt{-1}\partial\bar\partial u_0$ is positive. Consider the Calabi flow

$$\frac{\partial \varphi}{\partial t}=R_\varphi-\underline R.$$

Chen's short-time regularization conjecture. Given any initial $C^{1,1}$ Kähler potential, the Calabi flow admits a short-time solution and it immediately becomes smooth when $t>0$. This conjecture concerns existence and instantaneous smoothing from rough initial data. The paper studies this problem and proves short-time existence for broader classes of rough initial data, partially confirming the conjecture.