Uniform estimates for the solutions of the Schrödinger equation on the torus and regularity of semiclassical measures

Details Uniform estimates for the solutions of the Schrödinger equation on the torus and regularity of semiclassical measures Uniform estimates for the solutions of the Schrödinger equation on the torus and regularity of semiclassical measures

2011-10-29

arxiv.org/abs/1110.6521v2

Mathematics

Analysis of PDEs

11 pages; minor errors corrected; the presentation of the proof of Theorem 2.2 has been changed

Scientific paper

We establish uniform bounds for the solutions $e^{it\Delta}u$ of the Schr\"{o}dinger equation on arithmetic flat tori, generalising earlier results by J. Bourgain. We also study the regularity properties of weak-* limits of sequences of densities of the form $|e^{it\Delta}u_{n}|^{2}$ corresponding to highly oscillating sequences of initial data $(u_{n})$. We obtain improved regularity properties of those limits using previous results by N. Anantharaman and F. Maci\`a on the structure of semiclassical measures for solutions to the Schr\"{o}dinger equation on the torus.

Affiliated with

Also associated with

No associations

Rating

Uniform estimates for the solutions of the Schrödinger equation on the torus and regularity of semiclassical measures 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 Uniform estimates for the solutions of the Schrödinger equation on the torus and regularity of semiclassical measures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Uniform estimates for the solutions of the Schrödinger equation on the torus and regularity of semiclassical measures will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-200376