Two singular dynamics of the nonlinear Schrödinger equation on a plane domain

Geometric and Functional Analysis

Volumn 13, Issue 1, 2003, Pages 1-19

  Burq, N ^a   Gerard P ^a   Tzvetkov, N ^a  

^a UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038238334     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000390300000     Document Type: Article

References (21)

1. [Bo] J. BOURGAIN, Global Solutions of Nonlinear Schrödinger Equations, Colloq. Publications, American Math. Soc., 1999.
2. [BoW] J. BOURGAIN, W. WANG, Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity, Ann. Scuola Norm. Sup. Pisa Sci. 25 (1997), 197-215.
3. [BrG] H. BRÉZIS, T. GALLOUET, Nonlinear Schrödinger evolution equations, Nonlinear Analysis, Theory, Methods and Applications 4 (1980), 677-681.
4. [BGT1] N. BURQ, P. GÉRARD, N. TZVETKOV, Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds, preprint 2001.
5. d, Math. Res. Lett. 9 (2002), 323-335.
6. [C] T. CAZENAVE, An Introduction to Nonlinear Schrödinger Equations, 2nd edition, Textos de Métodos Matemáticos 26, 1993.
7. s, Nonlinear Anal. 14:10 (1990), 807-836.
8. [GV] J. GINIBRE, G. VELO, On a class of nonlinear Schrödinger equations, J. of Func. Anal. 32 (1979), 1-71.
9. [Gl] R.T. GLASSEY, On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations, J. of Math. Phys. 18 (1977), 1794-1797.
10. [H] L. HÖRMANDER, The Analysis of Linear Partial Differential Operators I, Springer-Verlag, 1983.
11. [K] O. KAVIAN, A remark on the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations, Trans. AMS 299 (1987), 193-203.
12. [KePV] C. KENIG, G. PONCE, L. VEGA, On the ill-posedness of some canonical dispersive equations, Duke Math. J. 106 (2001), 617-633.
13. [M1] F. MERLE, Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity, Comm. Math. Phys. 129 (1990), 223-240.
14. [M2] F. MERLE, Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equation with critical power, Duke Math. J. 69 (1993), 427-453.
15. [OT] T. OGAWA, Y. TSUTSUMI, Blow-up solutions for the nonlinear Schrödinger equation with quartic potential and periodic boundary conditions, Springer Lecture Notes in Math. 1450 (1990), 236-251.
16. [S] L. SCHWARTZ, Méthodes mathématiques pour les sciences physiques, Hermann, Paris, 1961.
17. [V] M. V. VLADIMIROV, On the solvability of mixed problem for a nonlinear equation of Schrödinger type, Sov. Math. Dokl. 29 (1984), 281-284.
18. [VlPT] S.N. VLASOV, L.V. PISKUNOVA, V.I. TALANOV, Averaged description of wave-beams in linear and nonlinear media (the method of moments) Izv. Vys. Uchebn. Zaved Radioflz. 14 (1971), 1353.
19. [W] G. WATSON, A Treatise on the Theory of Bessel Functions, 2nd edition, Cambridge Univ. Press, Cambridge, 1944.
20. [We] M. WEINSTEIN, Nonlinear Schrödinger equations and sharp interpolation estimates, Comm. Math. Phys. 87 (1983), 567-576.
21. [Z] V.E. ZAKHAROV, Collapse of Langmuir waves, Sov. Phys. JETP 35 (1972), 908-914.