Scaling limits in Kinetic theory

Summer School - Lyon - 2019

**Talk by Juan Velázquez** (University of Bonn)

*Homoenergetic solutions of Boltzmann equation*

In this talk I will discuss the properties of a class of solutions of the Boltzmann equation, the so-called homoenergetic solutions which were introduced by Galkin and Truesdell in the 1960s. These solutions are a particular type of non-equilibrium solutions of the Boltzmann equation. Therefore, they do not behave asymptotically for long times as Maxwellian distributions, at least for all the choices of the collision kernels. The current knowledge about the long time behaviour of the homoenergetic solutions as well as some conjectures and open problems will be discussed.