On quasilinear Maxwell equations in two dimensions
Robert Schippa, Roland Schnaubelt
TL;DR
This paper establishes new sharp Strichartz estimates for the 2D Maxwell system with rough coefficients, using phase space analysis, leading to improved local well-posedness results for quasilinear equations.
Contribution
It introduces a novel phase space approach using the FBI transform to derive Strichartz estimates for Maxwell equations with rough coefficients in two dimensions.
Findings
Sharp Strichartz estimates for 2D Maxwell with rough permittivity
Improved local well-posedness results for quasilinear Maxwell equations
Application of FBI transform to phase space analysis of Maxwell system
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.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Advanced Numerical Methods in Computational Mathematics · Electromagnetic Simulation and Numerical Methods