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1999 The initial value problem for the elliptic-hyperbolic Davey-Stewartson equation
Hiroyuki Chihara
J. Math. Kyoto Univ. 39(1): 41-66 (1999). DOI: 10.1215/kjm/1250517953

Abstract

We present the local and the global existence theorems for the elliptic-hyperbolic Davey-Stewartson equation which does not allows the classical energy estimates. To overcome this difficulty, we make use of the smoothing property of linear Schrödinger type equations which was obtained by S. Doi. Then under the smallness condition to $L^{2}$-norm of the initial data, we get the local solution. Moreover we show the global existence of small amplitude solutions by the a priori estimates for which the null gauge condition of Y. Tsutsumi plays an important role.

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Hiroyuki Chihara. "The initial value problem for the elliptic-hyperbolic Davey-Stewartson equation." J. Math. Kyoto Univ. 39 (1) 41 - 66, 1999. https://doi.org/10.1215/kjm/1250517953

Information

Published: 1999
First available in Project Euclid: 17 August 2009

zbMATH: 0947.35036
MathSciNet: MR1684172
Digital Object Identifier: 10.1215/kjm/1250517953

Subjects:
Primary: 35Q55
Secondary: 35M10

Rights: Copyright © 1999 Kyoto University

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Vol.39 • No. 1 • 1999
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