1.Course background and purpose：

This is an advanced course that conducts research ideas and technical machinery for the investigation of Boltzmann equations. We aim to prepare graduate students for the research of the Boltzmann equations.

2.Outline and speakers：

We shall start with the 89 annals paper of Diperna and Lions to introduce the most important ingredients of the Boltzmann equations. In particular, the basic conservation laws, H theorem and entropy inequalities. There are three useful types solution concepts : distributional solution, mild solution and renormalized solutions. We shall follow Diperna and Lions’s idea to show the advantages of these three concepts and see how they go well together to combine with other useful ideas to overcome the subtleties to obtain the L^1 existence theory of cut-off Boltzmann equations. We then connect it to our recent research work on steady state solutions of Boltzmann equations. Unlike the evolution equations on flat domains, we do not have the well-known velocity averaging lemma to help to gain the compactness in the construction of weak solution. Regarding the issue of steady state solution on bounded domain, we need new key features to improve the previous results in literature. We shall explore some new ideas according to our recent work in this course.