Derivation of the Half-Wave Maps Equation from Calogero--Moser Spin Systems

Enno Lenzmann, Jérémy Sok

We prove that the energy-critical half-wave maps equation \[ \partial_t \mathbf{S} =\mathbf{S} \times |\nabla| \mathbf{S}, \quad (t,x) \in \mathbb{R} \times \mathbb{T} \] arises as…