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arXiv · 1512.05197

Low regularity solutions for the (2+1) - dimensional Maxwell-Klein-Gordon equations in temporal gauge

Hartmut Pecher
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Abstract

The Maxwell-Klein-Gordon equations in 2+1 dimensions in temporal gauge are locally well-posed for low regularity data even below energy level. The corresponding (3+1)-dimensional case was considered by Yuan. Fundamental for the proof is a partial null structure in the nonlinearity which allows to rely on bilinear estimates in wave-Sobolev spaces by d'Ancona, Foschi and Selberg, on an $(L^p_x L^q_t)$ - estimate for the solution of the wave equation, and on the proof of a related result for the Yang-Mills equations by Tao.

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Hartmut Pecher. 2016-05-11. Low regularity solutions for the (2+1) - dimensional Maxwell-Klein-Gordon equations in temporal gauge. https://arxiv.org/abs/1512.05197

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