The Chern-Simons-Higgs and the Chern-Simons-Dirac equations in Fourier-Lebesgue spaces

Hartmut Pecher

Published 2018-11-21, updated 2018-11-28Version 2

The Chern-Simons-Higgs and the Chern-Simons-Dirac systems in Lorenz gauge are locally well-posed in suitable Fourier-Lebesgue spaces $\hat{H}^{s,r}$. Our aim is to minimize $s=s(r)$ in the range $1<r \le 2$ . If $r \to 1$ we show that we almost reach the critical regularity dictated by scaling. In the classical case $r=2$ the results are due to Huh and Oh. Crucial is the fact that the decisive quadratic nonlinearities fulfill a null condition.