Solvability and blow-up criterion of the thermomechanical Cucker-Smale-Navier-Stokes equations in the whole domain

We study local existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker–Smale (in short TCS) model coupled with incompressible Navier–Stokes (NS) equations in the whole space. The coupled system consists of the kinetic TCS equation for particle ensemble and the incompressible NS equations for a fluid via a drag force. For the strong solution, we investigate the blow-up mechanism for the coupled system, and we also study the global existence of a weak solution in the whole space.