Dispersive estimates for 2D-wave equations with critical potentials

2020/03/23 by Luca Fanelli, Fanelli, Luca, Junyong Zhang +3
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.2003.10356

We correct the error in previous version and strengthen the results. Comments are welcome. 37 Pages

openalex publication_date 2020/03/23 · arxiv created 2020/09/22 · arxiv updated 2020/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the 2D-wave equation with a scaling-critical electromagnetic potential. This problem is doubly critical, because of the scaling invariance of the model and the singularities of the potentials, which are not locally integrable. In particular, the diamagnetic phenomenon allows to consider negative electric potential which can be singular in the same fashion as the inverse-square potential. We prove sharp time-decay estimates in the purely magnetic case, and Strichartz estimates for the complete model, involving a critical electromagnetic field.

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