Cover

Title page

Chapter 1. Introduction

1.1. Main results

1.2. Relation with the Nordheim \index{Nordheim} equation

1.3. Plan of the paper

Chapter 2. Well-Posedness Results

2.1. Weak solutions with interacting condensate

2.2. Weak solutions with non interacting condensate

2.3. Mild solutions

2.4. Existence of bounded mild solutions \index{mild solution}

2.5. Existence of global weak solutions with interacting condensate \index{weak solution}

2.6. Stationary solutions

2.7. Weak solutions with non interacting condensate

Chapter 3. Qualitative behaviors of the solutions

3.1. Weak solutions with interacting condensate as 𝑡→∞

3.2. Energy transfer towards large values of 𝑘.

3.3. Detailed asymptotic behaviour of weak solutions

3.4. Finite time condensation

3.5. Finite time blow up \index{blow up} of bounded mild solutions

Chapter 4. Solutions without condensation: Pulsating behavior

4.1. Statement of the result

4.2. Proof of the result

Chapter 5. Heuristic arguments and open problems

5.1. Transport of the energy towards large values of 𝜔

5.2. Open problems

Chapter 6. Auxiliary results

Bibliography

Index

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