Title：Global well-posedness of the Boltzmann equation with large amplitude initial data

Speaker：Prof. Tong Yang（City University of Hong Kong）

Time：4:00-5:00 P.M. Apr.1, 2016

Location：Room 4318, Building No.4, Wushan Campus

Abstract: The global well-posedness of the Boltzmann equation with initial data of large amplitude has remained a long-standing open problem. In this paper, by developing a new $L^\infty_xL^1_{v}\cap L^\infty_{x,v}$  approach,   we prove the global existence and uniqueness of mild solutions to the Boltzmann equation in the whole space or torus for a class of initial data with bounded velocity-weighted $L^\infty$ norm under some  smallness condition on $L^1_xL^\infty_v$ norm as well as  defect mass, energy and entropy so that the initial data  allow  large amplitude oscillations. Both the hard and  soft potentials with angular cut-off are  considered,  and the large time behavior of solutions in $L^\infty_{x,v}$ norm with explicit rates of convergence is also studied. This is a joint work with Renjun Duan, Feimin Huang and Yong Wang.