基于Strichartz估计的三维克尔非线性Maxwell方程的适定性

arXiv: Analysis of PDEs Pub Date : 2021-08-17 DOI:10.5445/IR/1000136611

R. Schippa

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引用次数: 1

摘要

我们给出了三维拟线性麦克斯韦方程组的新的局部适定性结果，并着重讨论了克尔非线性。为此，通过对半波方程的共轭，证明了粗糙介电常数解的新的Strichartz估计。我们使用已知的strstrichartz估计与能量估计的组合来推导新的适定性结果。

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Well-posedness for Maxwell equations with Kerr nonlinearity in three dimensions via Strichartz estimates

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.

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arXiv: Analysis of PDEs

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