Low regularity solutions for the \((2+1)\)-dimensional Maxwell-Klein-Gordon equations in temporal gauge (Q334506)

The author studies the local well-posedness for the \((2+1)\)-dimensional Maxwell-Klein-Gordon equations in low regularity spaces. Most of the local well-posedness results were given in \(3+1\) dimensions or \(2+1\) dimensions in the Lorentz gauge, and this paper exclusively considers the \((2+1)\)-dimensional case in the temporal gauge. Making use of a partial null structure of the nonlinearities and bilinear estimates in wave-Sobolev spaces, and a powerful variant of Strichartz' estimates, the author proves the local well-posedness for data under minimal regularity assumptions, i.e., for initial data in \(H^s\times H^{s-1}\) where \(r>{1\over 4}\), \(l\geq s>\max\{{1\over 2} +{l\over 8}, {1\over 4}+{l\over 2},{1\over 4}+{r\over 2},{7\over 16}+{r\over 4}\}\), \(r+{1\over 2}>s\geq r -{1\over 2}\), \(s > l -{1\over 2}\).