A review on recent hypocoercivity results using Harris-type theorems

What is it about?

This paper explains how to use Harris-type theorems to obtain quantitative estimates on the long-time behaviour of kinetic equations and reviews recent results in this direction. We look at the applications of these theorems on some kinetic equations arising in physics and biology.

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Why is it important?

Applications of Harris-type theorems in kinetic theory is very recent and active research area. These theorems particularly helpful when a kinetic equation admits a non-explicit equilibrium, thus the uniqueness of the equilibrium cannot be obtained using classical H^1/L^2 type hypocoercivity methods.