Some mathematical problems in the kinetic theory for mixtures

Ana Jacinta Soares
October 8, 2019

The Kinetic Theory of gases is a branch of Statistical Mechanics which deals with non-equilibrium dilute gases, i.e. gas systems slightly removed from equilibrium. Instead of following the dynamics of each particle, the Kinetic Theory describes the evolution of the gas in terms of velocity distribution functions, which give information about the distribution of particles in the system as well as about the distribution of particle’s velocities.

The central equation in this theory is the so called Boltzmann equation, formulated by Ludwig Boltzmann in 1872. This equation describes the dynamics of the gas as a collection of many particles interacting through instantaneous elastic collisions.

When a gas mixture of several constituents is considered, the interactions among different constituents and the possibility of introducing chemical reactions induce many complexities in the equation and various interesting problems come out.

In this seminar, I will present some problems arising in this context that can be studied as a PhD research project.