Speaker
Jani Lukkarinen
(University of Helsinki)
Description
In a joint work with Jogia Bandyopadhyay and Antti Kupiainen,
we consider the kinetics of a three-dimensional fluid of weakly
interacting bosons with supercritical densities. More
precisely, we
consider the postulated nonlinear Boltzmann-Nordheim
equations for
this system, in a spatially homogeneous state which has an
isotropic
momentum distribution. The resulting evolution equations have a
surprisingly rich mathematical structure, where proper
definitions
play an important role. Elaborating on previous results, we
propose a
definition of the coupled equations for which the thermal
equilibrium states
are stationary. To test the validity of the equations, we
study the global
existence and uniqueness of solutions, as a problem about
return to
equilibrium from a perturbation of a thermal state with a
condensate. The
lessons learned from this enterprise ough
