The collisional kinetic theory and the Boltzmann equation play a central role in describing nonequilibrium processes in gas flows. They become essential when 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to maintain local equilibrium, and classical fluid dynamic models—such as the Navier-Stokes and Fourier laws—are no longer valid.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 regimes may arise due to microscopic effects or under rarefied conditions, typically characterized by a large Knudsen number, defined as the ratio of the mean free path to a characteristic observation length. The Boltzmann equation is known to capture 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—whose molecules possess 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 on the Boltzmann equation for polyatomic gases, based on a continuous internal energy framework. In the spatially homogeneous setting, assuming cut-off and hard potential-like collision 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 highlight the physical relevance of the proposed model by computing transport coefficients for polyatomic gas flows and comparing the results to experimental data.