We consider local well-posedness for the Maxwell-Chern-Simons-Higgs system in Lorenz gauge for data with minimal regularity assumptions in Fourier-Lebesgue spaces $\widehat{ H}^{ s,r}$ , where $\|u\|_{ \widehat{ H}^{ s,r}} := \| \langle \xi \rangle^s \widehat{ u}(\xi)\|_{ L^{ r'}}$ , and $r$ and $r'$ are dual exponents. We show that the gap between this regularity and the regularity with respect to scaling shrinks in the case $r>1$ , $r \to 1$ compared to the classical case $r=2$ .
Categories: math.AP