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The Cauchy problem for the system of Zakharov equations arising from ion-acoustic modes

Published online by Cambridge University Press:  14 November 2011

Guo Boling  and
Yuan Guangwei
Guo Boling
Affiliation:
Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, P.R. China
Yuan Guangwei
Affiliation:
Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, P.R. China
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Abstract

In this paper the initial value problem for a class of Zakharov equations arising from ion-acoustic modes is discussed. Without assuming the Cauchy data are small, we prove the existence and uniqueness of the global smooth solution for the problem via the so-called continuous method and delicate a priori estimates.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 4 , 1996 , pp. 811 - 820
Copyright
Copyright © Royal Society of Edinburgh 1996

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References

1Brezis, H. and Wainger, S.. A note on limiting cases of Sobolev imbeddings. Comm. Partial Differential Equations 5 (1980), 773–89.CrossRefGoogle Scholar
2Chanillo, S.. Sobolev inequalities involving divergence free maps. Comm. Partial Differential Equations 16 (1991), 1969–94.CrossRefGoogle Scholar
3Engler, H.. An alternative proof of the Brezis–Wainger inequality. Comm. Partial Differential Equations 14 (1989), 541–4.CrossRefGoogle Scholar
4Guo, B. L.. Global smooth solution for the system of Zakharov equations in nonhomogeneous medium. Northeastern Math. J. 6 (1990), 379–90.Google Scholar
5Shapiro, V. D. et al. Wave collapse at the lower-hybrid resonance. Phys. Fluids B 5 (1993), 3148–62.CrossRefGoogle Scholar
6Zhou, Y. L. and Guo, B. L.. Periodic boundary problem and initial value problem for the generalised Korteweg–de Vries systems of higher order. Ada Math. Sinica 27 (1984), 154–76 (in Chinese).Google Scholar