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
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. https://doi.org/10.57262/ade/1355703299
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