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

2015/12/16 by Pecher, Hartmut
#35L70 #35Q40 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1512.05197

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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