On the conditions to extend Ricci Bourguignon flow

In this paper,we study the extension problem of the Ricci Bourguignon flow on Riemannian manifolds. We show that the norm of the Weyl tensor of any smooth solution to the Ricci Bourguignon flow can be explicitly estimated in terms of its initial value on a given ball, a local uniform bound on the Ricci tensor. As an application, we show that along the Ricci Bourguignon flow, if the Ricci curvature is bounded, then the curvature operator is bounded.