On quasilinear Maxwell equations in two dimensions
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.
| 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 |