@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}, pages = {765--779}, publisher = {Elsevier}, volume = {23}, number = {5}, year = {2006}, doi = {10.1016/j.anihpc.2005.09.004}, zbl = {1122.35133}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2005.09.004/} }
TY - JOUR AU - Gérard, P. TI - The Cauchy problem for the Gross-Pitaevskii equation JO - Annales de l'I.H.P. Analyse non linéaire PY - 2006 SP - 765 EP - 779 VL - 23 IS - 5 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2005.09.004/ DO - 10.1016/j.anihpc.2005.09.004 LA - en ID - AIHPC_2006__23_5_765_0 ER -
%0 Journal Article %A Gérard, P. %T The Cauchy problem for the Gross-Pitaevskii equation %J Annales de l'I.H.P. Analyse non linéaire %D 2006 %P 765-779 %V 23 %N 5 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2005.09.004/ %R 10.1016/j.anihpc.2005.09.004 %G en %F 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) no. 5, pp. 765-779. doi : 10.1016/j.anihpc.2005.09.004. http://archive.numdam.org/articles/10.1016/j.anihpc.2005.09.004/
[1] Vortex rings for the Gross-Pitaevskii equation, J. Eur. Math. Soc. 6 (2004) 17-94. | EuDML | MR | Zbl
, , ,[2] Travelling waves for the Gross-Pitaevskii equation I, Ann. Inst. H. Poincaré Phys. Théor. 70 (1999) 147-238. | EuDML | Numdam | MR | Zbl
, ,[3] Nonlinear Schrödinger evolution equations, Nonlinear Anal. 4 (1980) 677-681. | MR | Zbl
, ,[4] Semilinear Schrödinger Equations, Courant Lecture Notes in Math., vol. 10, New York University, American Mathematical Society, Providence, RI, 2003. | MR | Zbl
,[5] Transition to dissipation in a model of superflow, Phys. Rev. Lett. 69 (1992) 1644-1647.
, , ,[6] Schrödinger group on Zhidkov spaces, Adv. Differential Equations 9 (2004) 509-538. | MR | Zbl
,[7] On a class of nonlinear Schrödinger equations, J. Funct. Anal. 32 (1979) 1-71. | MR | Zbl
, ,[8] The global Cauchy problem for the nonlinear Schrödinger equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 2 (1985) 309-327. | EuDML | Numdam | MR | Zbl
, ,[9] O. Goubet, Two remarks on solutions of Gross-Pitaevskii equations on Zhidkov spaces, Preprint, 2005. | MR | Zbl
[10] A non-existence result for supersonic travelling waves in the Gross-Pitaevskii equation, Comm. Math. Phys. 243 (2003) 93-103. | MR | Zbl
,[11] Decay of travelling waves in the Gross-Pitaevskii equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 21 (2004) 591-637. | Numdam | MR | Zbl
,[12] Limit at infinity and non-existence result for sonic travelling waves in the Gross-Pitaevskii equation, Differential Integral Equations 17 (2004) 1213-1232. | MR | Zbl
,[13] J. Math. Phys. 4 (1963) 195.
,[14] The Analysis of Linear Partial Differential Operators, vol. 1, Springer-Verlag, 1983.
,[15] On nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Phys. Théor. 46 (1987) 113-129. | Numdam | MR | Zbl
,[16] Endpoint Strichartz estimates, Amer. J. Math. 120 (1998) 955-980. | MR | Zbl
, ,[17] Decaying Kolmogorov turbulence in a model of superflow, Phys. Fluids 9 (1997) 2644-2669. | MR
, , ,[18] Sov. Phys. JETP 13 (1961) 451.
,[19] The Nonlinear Schrödinger Equation. Self-Focusing and Wave Collapse, Appl. Math. Sci., vol. 139, Springer-Verlag, 1999. | MR | Zbl
, ,[20] P.E. Zhidkov, The Cauchy problem for a nonlinear Schrödinger equation, Dubna, 1987.
[21] Korteweg-de Vries and Nonlinear Schrödinger Equations: Qualitative Theory, Lecture Notes in Math., vol. 1756, Springer-Verlag, 2001. | MR | Zbl
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