Subelliptic estimates for the inhomogeneous Boltzmann equation without cutoff

In this article we provide global subelliptic estimates for the Bolzmann equation without angular cutoff, and show that some global gain in the spatial coordinate is available although the corresponding operator is not elliptic in this direction. Due to the bad symbolic properties of the operator (in the microlocal sense), the proof uses the so-called Wick quantization and of some ideas coming from semi-classical analysis.

This is a joint work with W.-X. Li (Wuhan) and R. Alexandre (Shanghai and Brest).