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Phase separating solutions for two component systems in general planar domains

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Abstract

In this paper we consider a two component system of coupled non linear Schrödinger equations modeling the phase separation in the binary mixture of Bose–Einstein condensates and other related problems. Assuming the existence of solutions in the limit of large interspecies scattering length \(\beta \) the system reduces to a couple of scalar problems on subdomains of pure phases (Noris et al. in Commun Pure Appl Math 63:267–302, 2010). Here we show that given a solution to the limiting problem under some additional non degeneracy assumptions there exists a family of solutions parametrized by \(\beta \gg 1\).

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Acknowledgements

We would like to thank the referee for very careful and insightful reading of the manuscript.

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Authors and Affiliations

  1. Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático (UMI 2807 CNRS), Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile

    Michał Kowalczyk

  2. Dipartimento SBAI, Sapienza Università di Roma, Via Antonio Scarpa 16, 00161, Rome, Italy

    Angela Pistoia

  3. Dipartimento di Matematica, Università di Bari, Via Edoardo Orabona 4, 70125, Bari, Italy

    Giusi Vaira

Authors
  1. Michał Kowalczyk
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  2. Angela Pistoia
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  3. Giusi Vaira
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Correspondence to Michał Kowalczyk.

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Communicated by Andrea Mondino.

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M. Kowalczyk was partially funded by Chilean research grants FONDECYT 1210405 and ANID projects ACE210010 and FB210005. He also acknowledges the hospitality of the Sapienza University in Rome where part of this work was done during his visit in March 2019. A. Pistoia and G. Vaira were partially supported by project Vain-Hopes within the program VALERE: VAnviteLli pEr la RicErca.

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Kowalczyk, M., Pistoia, A. & Vaira, G. Phase separating solutions for two component systems in general planar domains. Calc. Var. 62, 142 (2023). https://doi.org/10.1007/s00526-023-02483-w

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