  In their fundamental work, B. Dubrovin and Y. Zhang, generalizing the
Virasoro equations for the genus 0 Gromov-Witten invariants, proved the
Virasoro equations for a descendent potential in genus 0 of an arbitrary
conformal Frobenius manifold. More recently, a remarkable system of partial
differential equations, called the open WDVV equations, appeared in the work of
A. Horev and J. P. Solomon. This system controls the genus 0 open Gromov-Witten
invariants. In our paper, for an arbitrary solution of the open WDVV equations,
satisfying a certain homogeneity condition, we construct a descendent potential
in genus 0 and prove an open analog of the Virasoro equations. We also present
conjectural open Virasoro equations in all genera and discuss some examples.
