On quasilinear Maxwell equations in two dimensions
Analysis of PDEs
2022-10-19 v2
Abstract
New sharp Strichartz estimates for the Maxwell system in two dimensions with rough permittivity and non-trivial charges are proved. We use the FBI transform to carry out the analysis in phase space. For this purpose, the Maxwell equations are conjugated to a system of half-wave equations with rough coefficients. For this system, Strichartz estimates are similarly derived as in previous work by Tataru on scalar wave equations with rough coefficients. We use the estimates to improve the local well-posedness theory for quasilinear Maxwell equations in two dimensions.
Cite
@article{arxiv.2105.06146,
title = {On quasilinear Maxwell equations in two dimensions},
author = {Robert Schippa and Roland Schnaubelt},
journal= {arXiv preprint arXiv:2105.06146},
year = {2022}
}
Comments
50 pages, accepted to Pure and Applied Analysis