Asymptotic Flocking Dynamics of Relativistic–Cucker–Smale Particles Immersed in Incompressible Navier–Stokes Equations

In this paper, we propose a coupled system that describes the interaction between the Relativistic–Cucker–Smale (RCS) model and the incompressible Navier–Stokes equations through a drag force on the 3D torus . The model captures the collective dynamics of high‐speed particles immersed in a low‐speed background fluid. We first establish the global existence of weak solutions for large initial data. Furthermore, under suitable assumptions, we prove that the coupled system exhibits exponential asymptotic alignment between the RCS particles and the surrounding fluid. The main analytical challenge arises from handling the strong nonlinearity induced by the relativistic velocity mapping.