Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

Local existence in time of small solutions to the elliptic-hyperbolic Davey-Stewartson system in the usual Sobolev space

Nakao Hayashia1 and Hitoshi Hirataa2

a1 Department of Applied Mathematics, Science University of Tokyo, 1–3, Kagurazaka, Shinjuku-ku, Tokyo 162, Japan E-mail address: nhayashi@rs.kagu.sut.ac.jp

a2 Department of Mathematics, Sophia University, 7–1, Kioicho, Chiyoda-ku, Tokyo 102, Japan E-mail address: h-hirata@mm.sophia.ac.jp

Abstract

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)