Local Cauchy Theory for the Boltzmann-Nordheim Equation
One of the most influential equations in the kinetic theory of gases is
the so-called Boltzmann equation, describing the time evolution of the probability
density of a particle in a classical dilute gas. The irrefutable appearance of
Quantum Mechanics, however, required a modification to this celebrated kinetic
equation, resulting in the Boltzmann-Nordheim equation.
In this presentation we will discuss a newly found local Cauchy Theory for a general
solution to the spatially homogeneous bosonic Boltzmann-Nordheim equation in any
dimension $d \geq 3$, a case of much interest due to the so-called Bose-Einstein
The methods used to achieve this theory are similar to those available for the
classical Boltzmann equation, yet are entangled with L^infty control that dominates
the difference between the classical and quantum kinetic equation.
Time permitting we will discuss some details about the existence of a global
solution to the equation.