Extensions to stochastic and relativistic kinetic flocking models

Develop stochastic and relativistic extensions of the phase-spatially extended kinetic Cucker–Smale model with nonconvex confining forces, together with corresponding well-posedness and weak-flocking analyses.

Background

The paper’s results concern a deterministic kinetic Cucker–Smale equation with attractive nonconvex confinement, fully noncompact data, and polynomial or exponential mechanical-energy tails. The conclusion explicitly identifies stochastic and relativistic versions as unresolved extensions.

Because the conclusion groups these extensions with the stated problem of uniqueness under polynomial tails and says that the questions are left for future work, this entry records the concrete extension problem rather than treating it as a generic future-work aspiration.