Global existence and long-time dynamics for Coulomb-gauge Chern–Simons–Dirac systems

Establish global existence and characterize the long-time behavior of solutions to the two-dimensional Chern–Simons–Dirac equation in Coulomb gauge, including the expected modified-scattering dynamics.

Background

Under the Coulomb gauge condition, the two-dimensional Chern–Simons–Dirac system reduces to a nonlinear Dirac equation with a Hartree-type nonlinearity. The paper notes that local well-posedness has been studied under several gauge choices, but that the global theory and asymptotic behavior remain unresolved. The Fourier multipliers of the Hartree-type terms have the same order-minus-one singularity near the origin as the Coulomb potential, so the system is regarded as scattering-critical and modified scattering is expected. The analysis developed for the Dirac–Hartree equation cannot be directly applied because one of the bilinear components lacks the relevant Dirac null structure.