Local well-posedness for the Maxwell-Chern-Simons-Higgs system in Fourier-Lebesgue spaces

TL;DR

This paper establishes local well-posedness for the Maxwell-Chern-Simons-Higgs system in Fourier-Lebesgue spaces, demonstrating improved regularity results as the space parameter approaches 1, compared to classical Sobolev spaces.

Contribution

It extends well-posedness results to Fourier-Lebesgue spaces, reducing the regularity gap near the scaling-critical threshold for the system.

Findings

Well-posedness in Fourier-Lebesgue spaces for r > 1

Reduced regularity gap compared to classical Sobolev spaces

Improved understanding of minimal regularity assumptions

Abstract

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 $r=2$ .