学术报告（何凌冰 5.27）

We consider the well-posedness for the non-cutoff Boltzmann equation with soft potentials when the initial datum is close to the 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 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.