Abstract
The sharp range of Sobolev spaces is determined in which the Cauchy problem for the classical Zakharov system is well-posed, which includes existence of solutions, uniqueness, per-sistence of initial regularity, and real-analytic dependence on the initial data. In addition, under a condition on the data for the Schrodinger equation at the lowest admissible regularity, global well-posedness and scattering are proved. The results cover energy-critical and energy-supercritical dimensions d > 4.