  Ginibre-Tsutsumi-Velo (1997) proved local well-posedness for the Zakharov
system for any dimension $d$, in the inhomogeneous Sobolev spaces $(u,n)\in
H^k(\mathbb{R}^d)\times H^s(\mathbb{R}^d)$ for a range of exponents $k$, $s$
depending on $d$. Here we restrict to dimension $d=1$ and present a few results
establishing local ill-posedness for exponent pairs $(k,s)$ outside of the
well-posedness regime. The techniques employed are rooted in the work of
Bourgain (1993), Birnir-Kenig-Ponce-Svanstedt-Vega (1996), and
Christ-Colliander-Tao (2003) applied to the nonlinear Schroedinger equation.
