Global dynamics of the thermomechanical Cucker–Smale ensemble immersed in incompressible viscous fluids

We study a global dynamics of the thermomechanical Cucker–Smale (TCS) particles immersed in incompressible viscous fluid. For this, we use a coupled system consisting of kinetic TCS equation for particles and incompressible Navier–Stokes for fluid via a drag force in three dimensions. We first show the global existence of weak solutions for large data, and then establish the global existence and uniqueness of strong solutions under a smallness assumption on the initial data. We also provide a priori estimate of large-time behavior of strong solutions which exhibits an exponential alignment between TCS particles and fluid asymptotically.