Boltzmann-Grad limit

We provide a rigorous derivation of the linear Boltzmann equation without cut-off starting from a system of particles interacting via a potential with infinite range as the number of particles N goes to infinity under the Boltzmann-Grad scaling. The …

We provide a rigorous derivation of the linear Boltzmann equation without cut-off starting from a system of particles interacting via a potential with infinite range as the number of particles N goes to infinity under the Boltzmann-Grad scaling. The …

The work of this thesis belongs to the field of partial differential equations. More specifically, it is linked to the problematic of scale changes in the context of kinetic of gas. Indeed, knowing that there exists different scales of description for a gas (microscopic, mesoscopic and macroscopic scale), we want to link these different associated scales in a context where some randomness acts, in initial data and/or distributed on all the time interval.