The Cauchy problem for the Gross–Pitaevskii equation
Annales de l'I.H.P. Analyse non linéaire (2006)
- Volume: 23, Issue: 5, page 765-779
- ISSN: 0294-1449
Access Full Article
topHow to cite
topGérard, P.. "The Cauchy problem for the Gross–Pitaevskii equation." Annales de l'I.H.P. Analyse non linéaire 23.5 (2006): 765-779. <http://eudml.org/doc/78711>.
@article{Gérard2006,
author = {Gérard, P.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {nonlinear Schrödinger equation; Gross-Pitaevskii equation; global well posedness; Strichartz estimates},
language = {eng},
number = {5},
pages = {765-779},
publisher = {Elsevier},
title = {The Cauchy problem for the Gross–Pitaevskii equation},
url = {http://eudml.org/doc/78711},
volume = {23},
year = {2006},
}
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
PB - Elsevier
VL - 23
IS - 5
SP - 765
EP - 779
LA - eng
KW - nonlinear Schrödinger equation; Gross-Pitaevskii equation; global well posedness; Strichartz estimates
UR - http://eudml.org/doc/78711
ER -
References
top- [1] Béthuel F., Orlandi G., Smets D., Vortex rings for the Gross–Pitaevskii equation, J. Eur. Math. Soc.6 (2004) 17-94. Zbl1091.35085MR2041006
- [2] Béthuel F., Saut J.C., Travelling waves for the Gross–Pitaevskii equation I, Ann. Inst. H. Poincaré Phys. Théor.70 (1999) 147-238. Zbl0933.35177MR1669387
- [3] Brezis H., Gallouët T., Nonlinear Schrödinger evolution equations, Nonlinear Anal.4 (1980) 677-681. Zbl0451.35023MR582536
- [4] Cazenave T., Semilinear Schrödinger Equations, Courant Lecture Notes in Math., vol. 10, New York University, American Mathematical Society, Providence, RI, 2003. Zbl1055.35003MR2002047
- [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 Equations9 (2004) 509-538. Zbl1103.35093MR2099970
- [7] Ginibre J., Velo G., On a class of nonlinear Schrödinger equations, J. Funct. Anal.32 (1979) 1-71. Zbl0396.35029MR533219
- [8] Ginibre J., Velo G., The global Cauchy problem for the nonlinear Schrödinger equation, Ann. Inst. H. Poincaré Anal. Non Linéaire2 (1985) 309-327. Zbl0586.35042MR801582
- [9] O. Goubet, Two remarks on solutions of Gross–Pitaevskii equations on Zhidkov spaces, Preprint, 2005. Zbl1128.35096MR2317389
- [10] Gravejat P., A non-existence result for supersonic travelling waves in the Gross–Pitaevskii equation, Comm. Math. Phys.243 (2003) 93-103. Zbl1044.35087MR2020221
- [11] Gravejat P., Decay of travelling waves in the Gross–Pitaevskii equation, Ann. Inst. H. Poincaré Anal. Non Linéaire21 (2004) 591-637. Zbl1057.35060MR2086751
- [12] Gravejat P., Limit at infinity and non-existence result for sonic travelling waves in the Gross–Pitaevskii equation, Differential Integral Equations17 (2004) 1213-1232. Zbl1150.35301MR2100023
- [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. Zbl0521.35002
- [15] Kato T., On nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Phys. Théor.46 (1987) 113-129. Zbl0632.35038MR877998
- [16] Keel M., Tao T., Endpoint Strichartz estimates, Amer. J. Math.120 (1998) 955-980. Zbl0922.35028MR1646048
- [17] Nore C., Abid M., Brachet M., Decaying Kolmogorov turbulence in a model of superflow, Phys. Fluids9 (1997) 2644-2669. Zbl1185.76669MR1467686
- [18] Pitaevskii L.P., Sov. Phys. JETP13 (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. Zbl0928.35157MR1696311
- [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. Zbl0987.35001MR1831831
Citations in EuDML Documents
top- Fabrice Béthuel, Philippe Gravejat, Didier Smets, Stability in the energy space for chains of solitons of the one-dimensional Gross-Pitaevskii equation
- V. Banica, L. Vega, On the Dirac delta as initial condition for nonlinear Schrödinger equations
- Thomas Alazard, Rémi Carles, WKB analysis for the Gross-Pitaevskii equation with non-trivial boundary conditions at infinity
- Evelyne Miot, Dynamique des points vortex dans une équation de Ginzburg-Landau complexe
- Mihai Mariş, Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity: some results and open problems
- Fabrice Béthuel, Philippe Gravejat, Jean-Claude Saut, Ondes progressives pour l’équation de Gross-Pitaevskii
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.