Space-time behavior of the solution to the Boltzmann equation with soft potentials

In this paper, we get the quantitative space-time behavior of full Boltzmann equation with soft potentials (−2<γ<0) in close to equilibrium setting, under some velocity decay assumption, but without any Sobolev regularity assumption on initial data. We find that both large time and spatial behaviors depend data exponent γ. The key step our strategy is obtain L∞ bound a suitable weighted directly, rather than using Green's function Duhamel's principle construct pointwise structure solution as [25]. This provides new thinking related study.