ABSTRACT

For the non-cutoff Boltzmann equation, we study the global well-posedness under the perturbation frame work around the equilibrium in spatially critical Besov spaces, following the recent work in the cutoff case by Duan-Liu-Xu. In the non-cutoff case, the triple norm introduced by AMUXY(Alexandre-MUkai-Xu-Yang) is a fundamental ingredient. Since the global solution is obtained as an extension of the time local solution, the mathematical rigorous proof of the local existence is also detailed in this talk, by showing commutator estimates between the nonlinear collision integral operator and the mollifier with respect to velocity derivative. The content of this talk is based on the joint work with S. Sakamoto.

[Light refreshments will be served outside the venue at 4:15-4:30 pm. Please come and join us.]