Global strong solutions for the thermomechanical Cucker–Smale–Navier–Stokes system in two dimensions

This paper is devoted to the analysis of the global well-posedness of strong solutions to a coupled system consisting of the thermomechanical Cucker–Smale model and the incompressible Navier–Stokes equations (TCS–NS) in R2. Employing an iterative construction, we first establish the local existence and uniqueness of strong solutions. Subsequently, by deriving refined energy estimates, controlling the support radii, and developing weighted a priori bounds, we obtain finite-time estimates for the fluid velocity that control the kinetic W1,∞-norm on every bounded time interval. These bounds allow the local strong solution to be continued globally. As a result, a global well-posedness theory is established for the two-dimensional TCS–NS system, valid for arbitrary initial data without any smallness assumptions.