Abstract
We study the regularity of stationary and time-dependent solutions to strong perturbations of the free Schrödinger equation on two-dimensional flat tori. This is achieved by performing a second microlocalization related to the size of the perturbation and by analyzing 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 closed geodesics.
Citation
Fabricio Macià. Gabriel Rivière. "Two-microlocal regularity of quasimodes on the torus." Anal. PDE 11 (8) 2111 - 2136, 2018. https://doi.org/10.2140/apde.2018.11.2111
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