a1 Department of Applied Mathematics, Science University of Tokyo, 1–3, Kagurazaka, Shinjuku-ku, Tokyo 162, Japan E-mail address: email@example.com
a2 Department of Mathematics, Sophia University, 7–1, Kioicho, Chiyoda-ku, Tokyo 102, Japan E-mail address: firstname.lastname@example.org
We study the initial value problem to the Davey-Stewartson system for the elliptic-hyperbolic case in the usual Sobolev space. We prove local existence and uniqueness H5/2 with a condition such that the L2 norm of the data is sufficiently small.
(Received January 09 1996)