On a dissipative Gross-Pitaevskii-type model for exciton-polariton condensates

Paolo Antonelli, Peter A. Markowich, Ryan Obermeyer, Jesus Sierra, CHRISTOF SPARBER

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5 Scopus citations


We study a generalized dissipative Gross-Pitaevskii-type model arising in the description of exciton-polariton condensates. We derive global in-time existence results and various a priori estimates for this model posed on the one-dimensional torus. Moreover, we analyze in detail the long-time behavior of spatially homogenous solutions and their respective steady states and present numerical simulations in the case of more general initial data. We also study the convergence to the corresponding adiabatic regime, which results in a single damped-driven Gross-Pitaveskii equation.
Original languageEnglish (US)
Pages (from-to)4317-4345
Number of pages29
Issue number11
StatePublished - Oct 2 2019

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The authors are grateful to the anonymous referee for helpful suggestions to improve upon an earlier version of this paper: in particular, we are grateful for pointing out the pointwise L∞-bound on n (see lemma 2.4) and for suggesting a Lyapunov-type functional similar to the one introduced in proposition 2.6.


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