  The Ostrovsky-Hunter equation provides a model for small-amplitude long waves
in a rotating fluid of finite depth. It is a nonlinear evolution equation. In
this paper we study the well-posedness for the Cauchy problem associated to
this equation within a class of bounded discontinuous solutions. We show that
we can replace the Kruzkov-type entropy inequalities by an Oleinik-type
estimate and prove uniqueness via a nonlocal adjoint problem. An implication is
that a shock wave in an entropy weak solution to the Ostrovsky-Hunter equation
is admissible only if it jumps down in value (like the inviscid Burgers
equation).
