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May/June 2011 Well posedness and stability in the periodic case for the Benney system
J. Angulo, A.J. Corcho, S. Hakkaev
Adv. Differential Equations 16(5/6): 523-550 (May/June 2011).

Abstract

We establish local well-posedness results in weak periodic function spaces for the Cauchy problem of the Benney system. The Sobolev space $H^{1/2}\times L^2$ is the lowest regularity attained and also we cover the energy space $H^{1}\times L^2$, where global well posedness follows from the conservation laws of the system. Moreover, we show the existence of a smooth explicit family of periodic travelling waves of dnoidal type and we prove, under certain conditions, that this family is orbitally stable in the energy space.

Citation

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J. Angulo. A.J. Corcho. S. Hakkaev. "Well posedness and stability in the periodic case for the Benney system." Adv. Differential Equations 16 (5/6) 523 - 550, May/June 2011.

Information

Published: May/June 2011
First available in Project Euclid: 17 December 2012

zbMATH: 1228.35215
MathSciNet: MR2816115

Subjects:
Primary: 35Q55, 35Q60

Rights: Copyright © 2011 Khayyam Publishing, Inc.

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Vol.16 • No. 5/6 • May/June 2011
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