Well-posedness for Maxwell equations with Kerr nonlinearity in three dimensions via Strichartz estimates
Abstract:
We show new local well-posedness results for quasilinear Maxwell equations in three spatial dimensions with an emphasis on the Kerr nonlinearity. For this purpose, new Strichartz estimates are proved for solutions with rough permittivity by conjugation to half-wave equations. We use the Strichartz estimates in a known combination with energy estimates to derive the new well-posedness results.
| Zugehörige Institution(en) am KIT | Institut für Analysis (IANA) Sonderforschungsbereich 1173 (SFB 1173) |
| Publikationstyp | Forschungsbericht/Preprint |
| Publikationsmonat/-jahr | 08.2021 |
| Sprache | Englisch |
| Identifikator | ISSN: 2365-662X KITopen-ID: 1000136611 |
| Verlag | Karlsruher Institut für Technologie (KIT) |
| Umfang | 21 S. |
| Serie | CRC 1173 Preprint ; 2021/36 |
| 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, Kerr nonlinearity |