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

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

2010-09-05

arxiv.org/abs/1009.0944v2

Mathematics

Analysis of PDEs

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Well-posedness and stability in the periodic case for the Benney system does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Well-posedness and stability in the periodic case for the Benney system, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Well-posedness and stability in the periodic case for the Benney system will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-297366