  This paper is devoted to studying the Cauchy problem for the Ostrovsky
equation \begin{eqnarray*}
  \partial_{x}\left(u_{t}-\beta \partial_{x}^{3}u
  +\frac{1}{2}\partial_{x}(u^{2})\right)
  -\gamma u=0, \end{eqnarray*} with positive $\beta$ and $\gamma $. This
equation describes the propagation of surface waves in a rotating oceanic flow.
We first prove that the problem is locally well-posed in
$H^{-\frac{3}{4}}(\R)$. Then we reestablish the bilinear estimate, by means of
the Strichartz estimates instead of calculus inequalities and Cauchy-Schwartz
inequalities. As a byproduct, this bilinear estimate leads to the proof of the
local well-posedness of the problem in $H^{s}(\R)$ for $ s>-\frac{3}{4}$, with
help of a fixed point argument.
