Large Time Behavior of Solutions to Kinetic Equations with Singular Angular Kernels

Most well-posedness theories for kinetic equations, especially the Boltzmann equation, are based on the Grad's angular cutoff assumption. However, for most of the particle interaction potentials, such as potentials of inverse power laws, the cross-sections have non-integrable singularity corresponding to the grazing collisions. Studies on the kinetic equations with singular kernels mainly focus on the regularizing effect on the solutions without the angular cutoff assumption.Since the large time behaviour of solutions to the kinetic equations with angular cutoff has been extensively investigated, the main concern of this project is to study this problem for the angular non-cutoff case. The investigators will study the time convergence to the global Maxwellian, or the nontrivial wave patterns without external forcing, or the nontrivial solution profile with external forcing.