In this paper we present a hydrodynamic model to describe the dynamics of para- and orthoexcitons in cuprous oxide at ultralow temperatures inside a stress induced potential trap. We take into account the finite lifetime of the excitons, the excitation process and exciton-phonon as well as exciton-exciton interaction. Furthermore, we model the two-body loss mechanism assuming an Auger-like effect and compare it to an alternative explanation which relies on the formation of biexcitons. We discuss in detail the influence on the numerical results and compare the predictions to experimental data.
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