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 $L_x^\infty L_v^1\cap L^\infty_{x,v}$ 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 $L_x^\infty L_v^1$ -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$L^\infty$-norm with explicit rates of convergence is also studied. Furthermore, I will also show you some regularity results.

[Light refreshments will be served outside the venue at 4:00-4:30 pm. Please come and join us.]