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

2021/08/30 by Pecher, Hartmut
#35L70 #35Q40 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2108.13279

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 \widehatH^s,r , where ‖u‖_\widehatH^s,r := ‖ ⟨ ξ⟩^s \widehatu(ξ)‖_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 → 1 compared to the classical case r=2 .

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