Local well-posedness of the two-dimensional Dirac-Klein-Gordon equations in Fourier-Lebesgue spaces

Abstract

The local well-posedness problem is considered for the Dirac-Klein-Gordon system in two space dimensions for data in Fourier-Lebesgue spaces ${\hat{H}}^{s,r}$ , where $\Vert f{\Vert }_{{\hat{H}}^{s,r}}=\Vert ⟨\xi {⟩}^s\hat{f}{\Vert }_{L^{r^{\prime }}}$ and $r$ and $r^{\prime }$ denote dual exponents. We lower the regularity assumptions on the data with respect to scaling improving the results of d'Ancona, Foschi and Selberg in the classical case $r=2$ . Crucial is the fact that the nonlinearities fulfill a null condition as detected by these authors.

arXiv comment10 pages, proof of Prop. 2.5 detailed