# CONFLUENTES MATHEMATICI

Global well-posedness of a system from quantum hydrodynamics for small data
Confluentes Mathematici, Tome 7 (2015) no. 2, pp. 7-17.

This article describes a joint work of the author with B.HaspotUmr Cnrs 7534, Université Paris Dauphine, place du Maréchal De Lattre De Tassigny 75775 Paris cedex 16 (France), haspot@ceremade.dauphine.fr on the existence and uniqueness of global solutions for the Euler-Korteweg equations in the special case of quantum hydrodynamics. Our aim here is to sketch how one can construct global small solutions of the Gross-Pitaevskii equation and use the so-called Madelung transform to convert these into solutions without vacuum of the quantum hydrodynamics. A key point is to bound the the solution of the Gross-Pitaevskii equation away from $0$, this condition is fullfilled thanks to recent scattering results.

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DOI : https://doi.org/10.5802/cml.21
Classification : 35A01,  35Q31,  35Q55,  76D45
@article{CML_2015__7_2_7_0,
author = {Corentin Audiard},
title = {Global well-posedness of a system from quantum hydrodynamics for small data},
journal = {Confluentes Mathematici},
pages = {7--17},
publisher = {Institut Camille Jordan},
volume = {7},
number = {2},
year = {2015},
doi = {10.5802/cml.21},
language = {en},
url = {https://cml.centre-mersenne.org/articles/10.5802/cml.21/}
}
Corentin Audiard. Global well-posedness of a system from quantum hydrodynamics for small data. Confluentes Mathematici, Tome 7 (2015) no. 2, pp. 7-17. doi : 10.5802/cml.21. https://cml.centre-mersenne.org/articles/10.5802/cml.21/

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