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

Published online by Cambridge University Press:  20 January 2009

Nakao Hayashi  and
Hitoshi Hirata
Nakao Hayashi
Affiliation:
Department of Applied Mathematics, Science University of Tokyo, 1–3, Kagurazaka, Shinjuku-ku, Tokyo 162, JapanE-mail address:nhayashi@rs.kagu.sut.ac.jp
Hitoshi Hirata
Affiliation:
Department of Mathematics, Sophia University, 7–1, Kioicho, Chiyoda-ku, Tokyo 102, JapanE-mail address:h-hirata@mm.sophia.ac.jp
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Abstract

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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.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 40 , Issue 3 , October 1997 , pp. 563 - 581
Copyright
Copyright © Edinburgh Mathematical Society 1997

References

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