2 research outputs found
On the 2d Zakharov system with L^2 Schr\"odinger data
We prove local in time well-posedness for the Zakharov system in two space
dimensions with large initial data in L^2 x H^{-1/2} x 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 L^2-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 Schroedinger
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
Schroedinger equation in dimension two - and it is optimal because
Glangetas-Merle's solutions blow up at that time.Comment: 30 pages, 2 figures. Minor revision. Title has been change