Global well-posedness of a system from quantum hydrodynamics for small data
Audiard, Corentin1
1 Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France
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 : 10.5802/cml.21
Classification : 35A01, 35Q31, 35Q55, 76D45
Audiard, Corentin 1

1 Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France 
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Audiard, Corentin. 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. http://www.numdam.org/articles/10.5802/cml.21/

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