Resumen
We prove local in time well-posedness for the Zakharov system in two space dimensions with large initial data in L2 × H-1/2 × H-3/2. This is the space of optimal regularity in the sense that the data-to-solution map fails to be smooth at the origin for any rougher pair of spaces in the L2-based Sobolev scale. Moreover, it is a natural space for the Cauchy problem in view of the subsonic limit equation, namely the focusing cubic nonlinear Schrödinger equation. The existence time we obtain depends only upon the corresponding norms of the initial data—a result which is false for the cubic nonlinear Schrödinger equation in dimension two—and it is optimal because Glangetas–Merle's solutions blow up at that time.