Regularity Theory for the Space Homogeneous Polyatomic Boltzmann Flow

In this paper, we study the polyatomic Boltzmann equation based on continuous internal energy, focusing on physically relevant collision kernels of the hard potentials type with integrable angular part. We establish three main results: smoothing effects of the gain collision operator, propagation of velocity and internal energy first-order derivatives of solutions, and exponential decay estimates for singularities of the initial data. These results ultimately lead to a decomposition theorem, showing that any solution splits into a smooth part and a rapidly decaying rough component.