Well posedness and stability in the periodic case for the Benney system
Well posedness and stability in the periodic case for the Benney system
复制标题
Benney 系统周期性情况下的适定性和稳定性
DOI：
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发表时间：
2010
影响因子：
1.4
通讯作者：
And S. Hakkaev
中科院分区：
文献类型：
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作者：
J. Angulo;A. Corcho;And S. Hakkaev
本文建立了Benney系统Cauchy问题在弱周期函数空间上的局部适定性结果。Sobolev空间$H^{1/2}\times L^2$是获得的最低正则性，我们也涵盖了能量空间$H^{1}\times L^2$，其中全局适定性遵循系统的守恒定律。此外，我们还证明了平面型周期行波的光滑显\emph{族的存在性}，并在一定条件下证明了该族在能量空间上是轨道稳定的。
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.