  Using recent work of Carrand on equilibrium states for the billiard map, and
bootstrapping via a "leapfrogging" method from a previous article of Baladi and
Demers, we construct the unique measure of maximal entropy for two-dimensional
finite horizon Sinai (dispersive) billiard flows (and show it is Bernoulli),
assuming that the topological entropy of the flow is strictly larger than s_0
log 2 where 0<s_0<1 quantifies the recurrence to singularities. This bound
holds in many examples (it is expected to hold generically).
