On the Linearized System of Equations for the Condensate-Normal Fluid Interaction Near the Critical Temperature

The Cauchy problem for the linearization around one of its equilibria of a non linear system of equations, arising in the kinetic theory of a condensed gas of bosons near the critical temperature, is solved for radially symmetric initial data. As time tends to infinity, the solutions are proved to converge to an equilibrium of the same linear system, determined by the conservation of total mass and energy. The asymptotic limit of the condensate's density is proved to be larger or smaller than its initial value under a simple and explicit criteria on the initial data. For a large set of initial data, and for values of the momentum variable near the origin, the linear approximation n(t) of the density of the normal fluid behaves instantaneously as the equilibria of the non linear system.

Automated summary

The Cauchy problem for the linearization around one of its equilibria of a non linear system of equations arising in the kinetic theory of a condensed gas of bosons near the critical temperature is solved for radially symmetric initial data. As time tends to infinity, the solutions are proved to converge to an equilibrium of the same linear system determined by the conservation of total mass and energy. The asymptotic limit of the condensate's density is proved to be larger or smaller than its initial value under a simple and explicit criteria on the initial data. For a large set of initial data and for values of the momentum variable near the origin, the linear approximation n(t) of the density of the normal fluid behaves instantaneously as the equilibria of the non linear system.