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.

Reçu le : 2015-02-03
Accepté le : 2015-02-09
Publié le : 2016-02-15
DOI : https://doi.org/10.5802/cml.21
Classification : 35A01,  35Q31,  35Q55,  76D45
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     author = {Corentin Audiard},
     title = {Global well-posedness of a system from quantum hydrodynamics for small data},
     journal = {Confluentes Mathematici},
     publisher = {Institut Camille Jordan},
     volume = {7},
     number = {2},
     year = {2015},
     pages = {7-17},
     doi = {10.5802/cml.21},
     language = {en},
     url = {cml.centre-mersenne.org/item/CML_2015__7_2_7_0/}
}
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/item/CML_2015__7_2_7_0/

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