Propagation of Moments and Sharp Convergence Rate for Inhomogeneous Non-cutoff Boltzmann Equation with Soft Potentials
Time: 2022-04-14
Published By: He Liu
Speaker(s): Jie JI (Tsinghua Unviersity)
Time: 16:00-17:30 April 28, 2022
Venue: Room 29, Quan Zhai, BICMR
We prove the well-posedness for the non-cutoff Boltzmann equation with soft potentials when the initial datum is close to the global Maxwellian and has only polynomial decay at the large velocities in $L^2$ space. As a result, we get the propagation of the exponential moments and the sharp rates of the convergence to the global Maxwellian which seems the first results for the original equation with soft potentials. The new ingredients of the proof lie in localized techniques, the semigroup method as well as the propagation of the polynomial and exponential moments in $L^2$ space.
