Light PhD Seminar: On a kinetic equation for the normal fluid-condensate interaction in a Bose gas

Abstract:
The kinetic equation commonly used to describe the evolution of the energy distribution function of a space-homogeneous, weakly interacting gas of Bosons, is the Nordheim equation; a quantum version of the classical Boltzmann equation.
In the isotropic case, it was proved in [1] that in finite time, weak solutions form a Dirac delta at zero energy for certain initial data. This concentration of parti- cles at low energies could be related to the formation of a Bose-Einstein condensate.
We are interested in the interaction between the condensed and non-condensed particles. We will present some mathematical results, comprising the existence of weak solutions, conservation laws, moment production, and condensation, for a kinetic equation that aims to describe such interaction process (cf. [2]).

References
[1] M. Escobedo, J.J.L. Velázquez, Finite time blow-up and condensation for the bosonic Nordheim equation, Inventiones mathematicae, 200, 761-847, (2015).
[2] E. Corté, M. Escobedo, On a system of equations for the normal fluid-condensate interaction in a Bose gas, https://arxiv.org/abs/1803.09964, (2018). 

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