Local well-posedness for Chern-Simons gauged O(3) sigma equations under the Lorenz gauge

2025/03/18 by Guanghui, Jin, Zhang, Huali
#35Q40 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary 35L15

paper · doi:10.48550/arxiv.2503.13871

Abstract

In this paper, we study the Cauchy problem for the Chern-Simons gauged O(3) sigma model under the Lorenz gauge condition. We prove the local well-posedness of solutions if the initial matter field and gauge field satisfy (\bmϕ₀, \bA₀) ∈ H^s(\R²)× H^s-\frac12(\R²), s>1, where the critical regularity for \bmϕ₀ is s_c=1. Our proof is based on identifying null forms within the system and utilizing bilinear estimates in wave-Sobolev space.

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