Mean Field Derivation of a System of Nonlocal Conservation Laws

ABSTRACT In this paper, we investigate the mean‐field derivation of a multispecies nonlocal conservation laws from an particle Liouville equation incorporating particle interactions. The convergence is established in a strong sense. First, a vanishing viscosity result is provided to demonstrate the convergence of the nonlocal viscous system to its associated nonlocal conservation laws, including both weak and strong convergence. Achieving strong convergence in the vanishing viscosity limit requires a sequence of delicate uniform estimates and Helly's compactness argument. Second, the relative entropy method is employed to justify the strong convergence to the mean field limit in the multispecies setting.