Milana Čolić: From Monatomic to Polyatomic: Mathematical Aspects of the Homogeneous Boltzmann Flow

The collisional kinetic theory and the Boltzmann equation play a central role in describing nonequilibrium processes in gas flows. They become essential when gas particle collisions are insufficient to maintain local equilibrium, and classical fluid dynamic models—such as the Navier-Stokes and Fourier laws—are no longer valid. Such insufficient collisions may arise due to microscopic effects or in rarefied regimes, typically characterized by a large Knudsen number, defined as the ratio between the mean free path and a characteristic observation length scale. The Boltzmann equation is known to describe the full range of Knudsen numbers and also serves as the starting point for deriving improved continuum models. While originally developed for single-species monatomic gases, the modeling and analysis of polyatomic gases—composed of molecules with internal degrees of freedom—has become an active area of research due to its high relevance in applications. In this talk, we present recent advances for the spatially homogeneous Boltzmann equation describing polyatomic gases, based on a continuous internal energy framework. Assuming cut-off and hard potential-like kernels, we discuss results on moment theory, well-posedness, and higher integrability. These results are comparable to the classical theory for monatomic gases in the homogeneous setting. Finally, we indicate the physical relevance of the proposed model through the computation of transport coefficients for polyatomic gas flows.