An improved local well-posedness result for the one-dimensional Zakharov system

The 1D Cauchy problem for the Zakharov system is shown to be locally well-posed for low regularity Schrodinger data u(0) is an element of (H-k,H-p) over cap and wave data (n(0), n(1)) is an element of (H-l,H-p) over cap x (H-l-1,H-p) over cap under certain assumptions on the parameters k, l and 1 < p <= 2, where parallel to u(0)parallel to<(H-k,H-p)over cap> := parallel to <xi >(k)(u(0)) over cap parallel to(Lp') generalizing the results for p = 2 by Ginibre, Tsutsumi and Velo. Especially we are able to improve the results from the scaling point of view, and also allow suitable k < 0, l < -1/2, i.e. data u(0) is not an element of L-2 and (n(0), n(1)) is not an element of H-1/2 x H-3/2, which was excluded in the case p = 2. (C) 2008 Elsevier Inc. All rights reserved.