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On
quasilinear Maxwell equations in two dimensions
Robert Schippa and Roland Schnaubelt |
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Vol. 4 (2022), No. 2, 313–365
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DOI: 10.2140/paa.2022.4.313
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Abstract |
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New sharp Strichartz estimates for the Maxwell system in two dimensions with rough permittivity and nontrivial 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 proved using methods similar to those in previous works 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. |
Keywords
Maxwell equations, Strichartz estimates, quasilinear wave
equations, rough coefficients, half wave equation, Kerr
nonlinearity, FBI transform, phase space analysis
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Mathematical Subject Classification
Primary: 35B65, 35L45
Secondary: 35Q61
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Milestones
Received: 17 May 2021
Accepted: 26 January 2022
Published: 16 October 2022
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Authors |
| Robert Schippa | |
| Department of Mathematics Karlsruhe Institute of Technology Karlsruhe Germany |
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| Roland Schnaubelt | |
| Department of Mathematics Karlsruhe Institute of Technology Karlsruhe Germany |
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