Local well-posedness for the (3+1)-dimensional Maxwell-Klein-Gordon equations in temporal gauge

Hartmut Pecher

Published 2016-08-09Version 1

This is a more or less straightforward adjustment of the paper arXiv:1512.05197 by the author for the 2+1 dimensional Maxwell-Klein-Gordon equations in temporal gauge to the 3+1 dimensional situation. They are shown to be locally well-posed for low regularity data even below energy level improving a result by Yuan. Fundamental for the proof is a partial null structure of the nonlinearity which allows to rely on bilinear estimates in wave-Sobolev spaces by d'Ancona, Foschi and Selberg, on an $(L^4_x L^2_t)$ - estimate for the solution of the wave equation, and on the proof of a related result for the Yang-Mills equations by Tao.