First Order Non-Instantaneous Corrections in Collisional Kinetic Alignment Models

Abstract In this work the standard kinetic theory assumption of instantaneous collisions is lifted. A model for higher order non-instantaneous alignment collisions is presented and studied in the asymptotic regime of short collision duration. A first order accurate approximative model is derived as a correction to the instantaneous limit. Rigorous results on its well-posedness and on the instantaneous limit are proven. The approximative model is a system of two equations. An equally accurate scalar approximation is suggested.