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arXiv · 1009.0944

Well-posedness and stability in the periodic case for the Benney system

J. Angulo·A. J. Corcho·And S. Hakkaev
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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 smooth explicit family of periodic travelling waves of \emph{dnoidal} type and we prove, under certain conditions, that this family is orbitally stable in the energy space.

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J. Angulo, A. J. Corcho, And S. Hakkaev. 2010-09-05. Well-posedness and stability in the periodic case for the Benney system. https://arxiv.org/abs/1009.0944

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