تقرير
Strichartz estimates for Maxwell equations on domains with perfectly conducting boundary conditions
| العنوان: | Strichartz estimates for Maxwell equations on domains with perfectly conducting boundary conditions |
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| المؤلفون: | Burq, Nicolas, Schippa, Robert |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs |
| الوصف: | We consider Maxwell equations on a smooth domain with perfectly conducting boundary conditions in isotropic media in two and three dimensions. In the charge-free case we recover Strichartz estimates due to Blair--Smith--Sogge for wave equations on domains up to endpoints. For the proof we suitably extend Maxwell equations over the boundary, which introduces coefficients on the full space with codimension-$1$ Lipschitz singularity. This system can be diagonalized to half-wave equations amenable to the results of Blair--Smith--Sogge. In two dimensions, we improve the local well-posedness of the Maxwell system with Kerr nonlinearity via Strichartz estimates. Comment: 74 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2304.13368 |
| رقم الأكسشن: | edsarx.2304.13368 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |