Two-microlocal regularity of quasimodes on the torus
Analysis of PDEs
2018-06-13 v1 Mathematical Physics
math.MP
Abstract
We study the regularity of stationary and time-dependent solutions to strong perturbations of the free Schr\"odinger equation on two-dimensional flat tori. This is achieved by performing a second microlocalization related to the size of the perturbation and by analysing concentration and nonconcentration properties at this new scale. In particular, we show that sufficiently accurate quasimodes can only concentrate on the set of critical points of the average of the potential along geodesics.
Cite
@article{arxiv.1708.08799,
title = {Two-microlocal regularity of quasimodes on the torus},
author = {Fabricio Macià and Gabriel Rivière},
journal= {arXiv preprint arXiv:1708.08799},
year = {2018}
}