Electron. J. Diff. Equ., Vol. 2014 (2014), No. 141, pp. 1-27.

Hydrodynamical form for the one-dimensional Gross-Pitaevskii equation

Haidar Mohamad

We establish a well-posedness result for the hydrodynamical form (HGP) of the one dimensional Gross-Pitaevskii equation (GP) via the classical form of this equation. The result established in this way proves that (HGP) is locally well-posed since the solution of (GP) can vanished at some $t\neq 0$.

Submitted February 17, 2014. Published June 18, 2014.
Math Subject Classifications: 35C07, 35C08.
Key Words: Non-linear Schrodinger equation; Gross-Pitaevskii equation.

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Haidar Mohamad
Laboratoire Jacques-Louis Lions
Université Pierre et Marie Curie,
Boîte Courrier 187, 75252 Paris Cedex 05, France
email: tartousi@ann.jussieu.fr

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