In this course we will introduce and discuss the basic questions in kinetic theory, and the methodical approaches to their solutions. In particular, we will focus on the following topics:

- Boltzmann equation: Cauchy problem and properties of solutions
- entropy and the H theorem
- equilibrium and convergence to equilibrium

Prerequisites: Functional Analysis

# Lectures

| **Date** | **Topics** (preliminary) |

**1** | 18.04. | Introduction, Hard Sphere Dynamics: Existence of Flow |

**2** | 25.04. | Hard Sphere Dynamics: Existence of Flow, Liouville Equation, BBGKY Hierarchy |

**3** | 02.05. | Hard Sphere Dynamics: BBGKY Hierarchy, Boltzmann Equation |

**4** | 23.05 | Boltzmann Equation: Scattering, Collision Operator |

**5** | 28.05. | Boltzmann Equation: Representations of the Boltzmann operator, Bobylev identity |

**6** | 30.05. | Boltzmann Equation: Conserved quantities and Boltzmann H functional |

**7** | 06.06. | Boltzmann Equation: Boltzmann H theorem |

**8** | 13.06. | Boltzmann Equation: Boltzmann H theorem |

**9** | 20.06. | Boltzmann Equation: Solutions of the homogeneous Boltzmann equation (Existence) |

**10** | 27.06. | Boltzmann Equation: Solutions of the homogeneous Boltzmann equation (Conservation laws and H theorem) |

**11** | 11.07. | Boltzmann Equation: Solutions of the homogeneous Boltzmann equation (H theorem) |

**12** | 18.07. | Kac Equation: Chaoticity, Convergence to Boltzmann Equation |

**Lecture Notes**

Chapter 1

Chapter 2

Chapter 3

Chapter 4

# Exercise Classes

# Projects

Throughout the lecture I propose some mini projects that can be presented as a seminar talk at the end of the semester.

Project 1 | Derivation of the BBGKY hierarchy for hard spheres |

Project 2 | Derivation of the Boltzmann kernel from classical scattering theory |

Project 3 | Weak solutions of the homogeneous Boltzmann equation |

Project 4 | Chaoticity in the Kac master equation |

Project 5 | Convergence to equilibrium in the Kac equation in L^2 |

Project 6 | Convergence to equilibrium in the Kac equation in relative entropy |

Project 7 | Transport equation: method of characteristics and DiPerna-Lions theory |

# Examination

Online registration (KIT Campus System) for the oral exam is now open until 31 July 2018.

Exams for the lecture will take place in August.

# References

## General Introduction/Boltzmann Equation

## Hard Sphere Dynamics

## Kac Equation

## Transport Equation