假設空間均勻分布的波茲曼方程有一存在於特定勒貝格積分空間的解，並利用二項式展開的類似手法對此解的矩作時間上的類指數估計。

The thesis is divided into three parts. It includes a brief introduction of
the collision kernel, and the uses of the tools in X. Lu, C. Mouhot, <On measure solutions of the Boltzmann equation, part I: moment production and stability estimates.> to derive
the result for a solution of spatially homogeneous Boltzmann equation in
Lebesgue p-integrable space with finite initial moment and makes it to be
controlled by an exponentially like function as time goes on. And after the
conclusion comes along some appendices which make the thesis more clear
on its way to the final work.

1 Introduction 1
1.1 One-particle Distribution . . . . . . . . . . 1
1.2 Discussion of Collision kernel . . . . . . . . . . 4

2 Moment Estimate
2.1 Setting . . . . . . . . . . 7
2.2 Lemmas . . . . . . . . . . 10
2.3 Theorem . . . . . . . . . . 16

3 Conclusion

Appendices
A Tools A . . . . . . . . . . 22
B Tools B . . . . . . . . . . 25
Reference

A. V. Bobylev, I. M. Gamba, V. A. Panferov, Moment Inequalities and High-Energy Tails for Boltzmann Equations with Inelastic Interactions. J. Stat.Phys, v.116, (2004), 1651-1682.

C. Cercignani, The Boltzmann equation and its applications. Springer-Verlag,New York, 1998.

C. Villani, A review of mathematical topics in Collisional Kinetic theory.In: Handbook of mathematical
fluid dynamics, v. I, pp. 71305. Amsterdam:North-Holland 2002.

S. Harris, An Introduction to the Theory of the Boltzmann Equation. Dover Publications, 2011.

X. Lu, C. Mouhot, On measure solutions of the Boltzmann equation, part I:moment production and stability estimates. J. Differential Equations 252, 4(2012), 3305-3363.