Geodesic
Hydrodynamical form for the one-dimensional Gross-Pitaevskii equation
Electronic journal of differential equations, Tome 2014 (2014)
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 $t\neq 0$.
Classification : 35C07, 35C08
Keywords: non-linear Schrödinger equation, Gross-Pitaevskii equation 
@article{EJDE_2014__2014__a116,
     author = {Mohamad,  Haidar},
     title = {Hydrodynamical form for the one-dimensional {Gross-Pitaevskii} equation},
     journal = {Electronic journal of differential equations},
     year = {2014},
     volume = {2014},
     zbl = {1297.35085},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a116/}
}
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Mohamad,  Haidar. Hydrodynamical form for the one-dimensional Gross-Pitaevskii equation. Electronic journal of differential equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a116/