The Cauchy problem for the Gross-Pitaevskii equation
Gérard, P.
Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006), p. 765-779 / Harvested from Numdam
@article{AIHPC_2006__23_5_765_0,
     author = {G\'erard, P.},
     title = {The Cauchy problem for the Gross-Pitaevskii equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {23},
     year = {2006},
     pages = {765-779},
     doi = {10.1016/j.anihpc.2005.09.004},
     zbl = {05072661},
     zbl = {1122.35133},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2006__23_5_765_0}
}
Gérard, P. The Cauchy problem for the Gross-Pitaevskii equation. Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) pp. 765-779. doi : 10.1016/j.anihpc.2005.09.004. http://gdmltest.u-ga.fr/item/AIHPC_2006__23_5_765_0/

[1] Béthuel F., Orlandi G., Smets D., Vortex rings for the Gross-Pitaevskii equation, J. Eur. Math. Soc. 6 (2004) 17-94. | MR 2041006 | Zbl 1091.35085

[2] Béthuel F., Saut J.C., Travelling waves for the Gross-Pitaevskii equation I, Ann. Inst. H. Poincaré Phys. Théor. 70 (1999) 147-238. | Numdam | MR 1669387 | Zbl 0933.35177

[3] Brezis H., Gallouët T., Nonlinear Schrödinger evolution equations, Nonlinear Anal. 4 (1980) 677-681. | MR 582536 | Zbl 0451.35023

[4] Cazenave T., Semilinear Schrödinger Equations, Courant Lecture Notes in Math., vol. 10, New York University, American Mathematical Society, Providence, RI, 2003. | MR 2002047 | Zbl 1055.35003

[5] Frisch T., Pomeau Y., Rica S., Transition to dissipation in a model of superflow, Phys. Rev. Lett. 69 (1992) 1644-1647.

[6] Gallo C., Schrödinger group on Zhidkov spaces, Adv. Differential Equations 9 (2004) 509-538. | MR 2099970 | Zbl 1103.35093

[7] Ginibre J., Velo G., On a class of nonlinear Schrödinger equations, J. Funct. Anal. 32 (1979) 1-71. | MR 533219 | Zbl 0396.35029

[8] Ginibre J., Velo G., The global Cauchy problem for the nonlinear Schrödinger equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 2 (1985) 309-327. | Numdam | MR 801582 | Zbl 0586.35042

[9] O. Goubet, Two remarks on solutions of Gross-Pitaevskii equations on Zhidkov spaces, Preprint, 2005. | MR 2317389 | Zbl 1128.35096

[10] Gravejat P., A non-existence result for supersonic travelling waves in the Gross-Pitaevskii equation, Comm. Math. Phys. 243 (2003) 93-103. | MR 2020221 | Zbl 1044.35087

[11] Gravejat P., Decay of travelling waves in the Gross-Pitaevskii equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 21 (2004) 591-637. | Numdam | MR 2086751 | Zbl 1057.35060

[12] Gravejat P., Limit at infinity and non-existence result for sonic travelling waves in the Gross-Pitaevskii equation, Differential Integral Equations 17 (2004) 1213-1232. | MR 2100023 | Zbl 1150.35301

[13] Gross E.P., J. Math. Phys. 4 (1963) 195.

[14] Hörmander L., The Analysis of Linear Partial Differential Operators, vol. 1, Springer-Verlag, 1983.

[15] Kato T., On nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Phys. Théor. 46 (1987) 113-129. | Numdam | MR 877998 | Zbl 0632.35038

[16] Keel M., Tao T., Endpoint Strichartz estimates, Amer. J. Math. 120 (1998) 955-980. | MR 1646048 | Zbl 0922.35028

[17] Nore C., Abid M., Brachet M., Decaying Kolmogorov turbulence in a model of superflow, Phys. Fluids 9 (1997) 2644-2669. | MR 1467686 | Zbl pre05179339

[18] Pitaevskii L.P., Sov. Phys. JETP 13 (1961) 451.

[19] Sulem C., Sulem P.L., The Nonlinear Schrödinger Equation. Self-Focusing and Wave Collapse, Appl. Math. Sci., vol. 139, Springer-Verlag, 1999. | MR 1696311 | Zbl 0928.35157

[20] P.E. Zhidkov, The Cauchy problem for a nonlinear Schrödinger equation, Dubna, 1987.

[21] Zhidkov P.E., Korteweg-de Vries and Nonlinear Schrödinger Equations: Qualitative Theory, Lecture Notes in Math., vol. 1756, Springer-Verlag, 2001. | MR 1831831 | Zbl 0987.35001