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On quasilinear Maxwell equations in two dimensions

Schippa, Robert; Schnaubelt, Roland

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 which 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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Volltext §
DOI: 10.5445/IR/1000132767
Veröffentlicht am 14.05.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 05.2021
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000132767
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 49 S.
Serie CRC 1173 Preprint ; 2021/21
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter Maxwell equations, Strichartz estimates, quasilinear wave equations, rough coefficients, half wave equation, FBI transform
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