We consider a generalized Ricci flow with a given (not necessarily closed) three-form and establish higher-derivative estimates for compact manifolds. As an application, we prove the compactness theorem for this generalized Ricci flow. Similar results still hold for a more generalized Ricci flow.
"Generalized Ricci flow, I: Higher-derivative estimates for compact manifolds." Anal. PDE 5 (4) 747 - 775, 2012. https://doi.org/10.2140/apde.2012.5.747