A refined global well-posedness result for Schrodinger equations with derivative

Details A refined global well-posedness result for Schrodinger equations with derivative A refined global well-posedness result for Schrodinger equations with derivative

2001-10-02

arxiv.org/abs/math/0110026v2

Mathematics

Analysis of PDEs

21 pages, no figures, submitted, Siam J. Math

Scientific paper

In this paper we prove that the 1D Schr\"odinger equation with derivative in the nonlinear term is globally well-posed in $H^{s}$, for $s>\frac12$ for data small in $L^{2}$. To understand the strength of this result one should recall that for $s<\frac12$ the Cauchy problem is ill-posed, in the sense that uniform continuity with respect to the initial data fails. The result follows from the method of almost conserved energies, an evolution of the ``I-method'' used by the same authors to obtain global well-posedness for $s>\frac23$. The same argument can be used to prove that any quintic nonlinear defocusing Schr\"odinger equation on the line is globally well-posed for large data in $H^{s}$, for $s>\frac12$.

Affiliated with

Also associated with

No associations

Rating

A refined global well-posedness result for Schrodinger equations with derivative 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 A refined global well-posedness result for Schrodinger equations with derivative, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A refined global well-posedness result for Schrodinger equations with derivative will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-60675