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  • Séminaire Laurent Schwartz — EDP et applications
  • Année 2021-2022
  • Exposé no. 17
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A uniqueness result for travelling waves in the Gross-Pitaevskii equation
Eliot Pacherie1
1 NYUAD Research Institute, New York University Abu Dhabi, PO Box 129188, Abu Dhabi, UAE
Séminaire Laurent Schwartz — EDP et applications (2021-2022), Exposé no. 17, 16 p.
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This note is a summary of a series of papers [12], [13] and [14], done in collaboration with David Chiron. In them, we establish the uniqueness of the energy minimizer at fixed large momentum for the 2 dimensional Gross-Pitaevskii equation, up to the natural invariances of the problem. The minimizer is a nonradial travelling wave with a small speed, behaving like two well separated vortices. Here, we summarize the key steps of the proof, highlighting the arguments that can be used for similar problems in other equations.

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Publié le : 2022-06-22
DOI : 10.5802/slsedp.148
Affiliations des auteurs :
Eliot Pacherie 1

1 NYUAD Research Institute, New York University Abu Dhabi, PO Box 129188, Abu Dhabi, UAE
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@article{SLSEDP_2021-2022____A2_0,
     author = {Eliot Pacherie},
     title = {A uniqueness result for travelling waves in the {Gross-Pitaevskii} equation},
     journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
     note = {talk:17},
     pages = {1--16},
     publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2021-2022},
     doi = {10.5802/slsedp.148},
     language = {en},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.148/}
}
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JO  - Séminaire Laurent Schwartz — EDP et applications
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PY  - 2021-2022
SP  - 1
EP  - 16
PB  - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
UR  - https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.148/
DO  - 10.5802/slsedp.148
LA  - en
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%0 Journal Article
%A Eliot Pacherie
%T A uniqueness result for travelling waves in the Gross-Pitaevskii equation
%J Séminaire Laurent Schwartz — EDP et applications
%Z talk:17
%D 2021-2022
%P 1-16
%I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
%U https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.148/
%R 10.5802/slsedp.148
%G en
%F SLSEDP_2021-2022____A2_0
Eliot Pacherie. A uniqueness result for travelling waves in the Gross-Pitaevskii equation. Séminaire Laurent Schwartz — EDP et applications (2021-2022), Exposé no. 17, 16 p. doi : 10.5802/slsedp.148. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.148/
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