I present a theorem that states stretched exponential decay of correlations for planar dispersing billiard flows (with finite horizon and no corner point). This correlation decay is formulated in the form of an "equidistribution" statement for a class of initial distributions. The important feature of the theorem is that these initial distributions need not be absolutely continuous: they can be concentrated on a single unstable curve (they are so-called standard pairs). The motivation is applicability in heat a conduction model with separation of time scales. I plan to present this motivation and the key steps of the proof - which is based on a theorem of Nikolai Chernov about stretched exponential correlation decay for observables with better regularity. The result is joint with Péter Bálint, Péter Nándori and Domokos Szász.