Local well-posedness for the Zakharov system on multidimensional torus
  The initial value problem of the Zakharov system on two dimensional torus with general period is shown to be locally well-posed in the Sobolev spaces of optimal regularity, including the energy space. Proof relies on a standard iteration argument using the Bourgain norms. The same strategy is also applicable to three and higher dimensional cases. 
Nobu Kishimoto
math.AP