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GLOBAL WELL-POSEDNESS FOR THE GENERALISED FOURTH-ORDER SCHRÖDINGER EQUATION

Part of: Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  07 February 2012

YUZHAO WANG
YUZHAO WANG*
Affiliation:
Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, PR China (email: [email protected])
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Abstract

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We study the Cauchy problem for the generalised fourth-order Schrödinger equation for data u0 in critical Sobolev spaces . With small initial data we obtain global well-posedness results. Our proof relies heavily on the method developed by Kenig et al. [‘Well-posedness and scattering results for the generalised Korteweg–de Vries equation via the contraction principle’, Commun. Pure Appl. Math.46 (1993), 527–620].

Keywords

fourth-orderSchrödinger equationglobal well-posedness

MSC classification

Secondary: 35Q53: KdV-like equations (Korteweg-de Vries)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 85 , Issue 3 , June 2012 , pp. 371 - 379
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

References

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