On the Boltzmann equation, quantitative studies and hydrodynamical limits

Briant, Marc (2014-11-11)


The present thesis deals with the mathematical treatment of kinetic theory and focuses more precisely on the Boltzmann equation. We investigate several properties of the solutions to the latter equation: their positivity and their hydrodynamical limits for instance. We also study the local Cauchy problem for a quantic version of the Boltzmann equation.