On the periodic Korteweg-de Vries equation: a normal form approach

Details On the periodic Korteweg-de Vries equation: a normal form approach On the periodic Korteweg-de Vries equation: a normal form approach

2011-08-10

arxiv.org/abs/1108.2249v2

Mathematics

Analysis of PDEs

Minor revisions in the abstract and the introduction. Added one reference item

Scientific paper

This paper discusses an improved smoothing phenomena for low-regularity solutions of the Korteweg-de Vries (KdV) equation in the periodic settings by means of normal form transformation. As a result, the solution map from a ball on $H^{-1/2+}$ to $C_0^t ([0,T], H^{-1/2+})$ can be shown to be Lipschitz in a $H^{0+}_x$ topology, where the Lipschitz constant only depends on the rough norm $\|u_0\|_{H^{-1/2+}}$ of the initial data. A similar episode has been observed in a recent paper on 1D quadratic Schr\"odinger equation in low-regularity setting.

Affiliated with

Also associated with

No associations

Rating

On the periodic Korteweg-de Vries equation: a normal form approach 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 the periodic Korteweg-de Vries equation: a normal form approach, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the periodic Korteweg-de Vries equation: a normal form approach will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-665943