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On the Well-Posedness of Two Driven-Damped Gross–Pitaevskii-Type Models for Exciton-Polariton Condensates

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Abstract

We study the well-posedness of two systems modeling the non-equilibrium dynamics of pumped decaying Bose–Einstein condensates. In particular, we present the local theory for rough initial data using the Fourier restricted norm method introduced by Bourgain. We extend the result globally for initial data in \(L^{2}\).

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Acknowledgements

JS acknowledges financial support from the Austrian Science Fund (FWF) grant F65, the Vienna Science and Technology Fund (WWTF) project SEQUEX, and CONACYT Mexico through its program Estancias Posdoctorales por Mexico. JM acknowledges financial support from the Austrian Science Fund (FWF) grant W1245.

Funding

JS acknowledges financial support from the Austrian Science Fund (FWF) grant F65, the Vienna Science and Technology Fund (WWTF) project SEQUEX, and CONACYT Mexico through its program Estancias Posdoctorales por Mexico. JM acknowledges financial support from the Austrian Science Fund (FWF) grant W1245.

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Authors and Affiliations

  1. Research Platform MMM “Mathematics-Magnetism-Materials” c/o Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria

    Jakob Möller

  2. Wolfgang Pauli Institute c/o Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria

    Jesus Sierra

  3. Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, CP 04510, Mexico City, Mexico

    Jesus Sierra

Authors
  1. Jakob Möller
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  2. Jesus Sierra
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Both J.M. and J.S. contributed to the redaction and review of the manuscript.

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Correspondence to Jesus Sierra.

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Möller, J., Sierra, J. On the Well-Posedness of Two Driven-Damped Gross–Pitaevskii-Type Models for Exciton-Polariton Condensates. J Dyn Diff Equat (2024). https://doi.org/10.1007/s10884-024-10359-6

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  • DOI: https://doi.org/10.1007/s10884-024-10359-6

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