On well-posedness and wave operator for the gKdV equation

Details On well-posedness and wave operator for the gKdV equation On well-posedness and wave operator for the gKdV equation

2012-04-25

arxiv.org/abs/1204.5688v1

Mathematics

Analysis of PDEs

11 pages. To appear Bulletin des Sciences Math\'ematiques

Scientific paper

We consider the generalized Korteweg-de Vries (gKdV) equation $\partial_t u+\partial_x^3u+\mu\partial_x(u^{k+1})=0$, where $k>4$ is an integer number and $\mu=\pm1$. We give an alternative proof of the Kenig, Ponce, and Vega result in \cite{kpv1}, which asserts local and global well-posedness in $\dot{H}^{s_k}(\R)$, with $s_k=(k-4)/2k$. A blow-up alternative in suitable Strichatz-type spaces is also established. The main tool is a new linear estimate. As a consequence, we also construct a wave operator in the critical space $\dot{H}^{s_k}(\R)$, extending the results of C\^ote [2].

Affiliated with

Also associated with

No associations

Rating

On well-posedness and wave operator for the gKdV equation 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 On well-posedness and wave operator for the gKdV equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On well-posedness and wave operator for the gKdV equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-140034