| Abstract: |
| We establish the local and global well-posedness of weak and strong solutions for second-order fractional mean-field SDEs. These equations involve singular or distribution interaction kernels and measure initial values, with examples including Newton or Coulomb potentials, Riesz potentials, Biot-Savart law, among others. Our analysis relies on the theory of anisotropic Besov spaces. Building on the well-posedness results of the McKean-Vlasov equations, we investigate the propagation of chaos for moderately interacting particle systems with singular kernels and derive quantitative convergence rates. |
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