Existence and regularity for a model of viscous oriented fluid accounting for second-neighbor spin-to-spin interactions

We discuss the representation of the dynamics of incompressible, viscous fluids with spin structure, accounting for second-neighbor spin-to-spin interactions. Then, we focus attention on the minimal extension of the spin- to-spin interaction structure emerging from the second-neighbor setting. For a penalized version of it we prove eventually an existence theorem and discuss regularity.