On nonlinear Schrödinger equations in exterior domains
Annales de l'I.H.P. Analyse non linéaire (2004)
- Volume: 21, Issue: 3, page 295-318
- ISSN: 0294-1449
Access Full Article
topHow to cite
topBurq, N, Gérard, P, and Tzvetkov, N. "On nonlinear Schrödinger equations in exterior domains." Annales de l'I.H.P. Analyse non linéaire 21.3 (2004): 295-318. <http://eudml.org/doc/78620>.
@article{Burq2004,
author = {Burq, N, Gérard, P, Tzvetkov, N},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {nonlinear Schrödinger; smoothing effect; non-trapping; dispersive equations; global existence and uniqueness},
language = {eng},
number = {3},
pages = {295-318},
publisher = {Elsevier},
title = {On nonlinear Schrödinger equations in exterior domains},
url = {http://eudml.org/doc/78620},
volume = {21},
year = {2004},
}
TY - JOUR
AU - Burq, N
AU - Gérard, P
AU - Tzvetkov, N
TI - On nonlinear Schrödinger equations in exterior domains
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2004
PB - Elsevier
VL - 21
IS - 3
SP - 295
EP - 318
LA - eng
KW - nonlinear Schrödinger; smoothing effect; non-trapping; dispersive equations; global existence and uniqueness
UR - http://eudml.org/doc/78620
ER -
References
top- [1] Ben Artzi M, Klainerman S, Decay and regularity for the Schrödinger equation, J. Anal. Math.58 (1992) 25-37. Zbl0802.35057MR1226935
- [2] Bergh J, Löfstrom J, Interpolation Spaces, Springer-Verlag, 1976. Zbl0344.46071
- [3] Bourgain J, Global Solutions of Nonlinear Schrödinger Equations, Colloq. Publications, American Math. Soc, 1999. Zbl0933.35178MR1691575
- [4] Bourgain J, Problems in Hamiltonian PDE's. GAFA 2000 (Tel Aviv, 1999), Geom. Funct. Anal. (Special Volume, Part I) (2000) 32-56. Zbl1050.35016MR1826248
- [5] Brézis H, Gallouet T, Nonlinear Schrödinger evolution equations, Nonlinear Anal.4 (1980) 677-681. Zbl0451.35023MR582536
- [6] Burq N, Contrôle de l'équation des ondes dans des ouverts peu réguliers, Asymptotic Anal.14 (1997) 157-191. Zbl0892.93009MR1451210
- [7] Burq N, Décroissance de l'énergie locale de l'équation des ondes pour le problème extérieur et absence de résonance au voisinage du réel, Acta Math.180 (1998) 1-29. Zbl0918.35081MR1618254
- [8] Burq N, Semi-classical estimates for the resolvent in nontrapping geometries, Internat. Math. Res. Notices (2002) 221-241. Zbl1161.81368MR1876933
- [9] N. Burq, P. Gérard, N. Tzvetkov, Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds, Amer. J. Math., in press. Zbl1067.58027MR2058384
- [10] Burq N, Gérard P, Tzvetkov N, The Cauchy problem for the nonlinear Schrödinger equation on a compact manifold, Proceedings of the Öresund Symposium on Partial Differential Equations, Lund, May 23–25, 2002, J. Nonlinear Math. Phys.10 (2003) 12-27, Supplement 1. MR2063542
- [11] Burq N, Gérard P, Tzvetkov N, Two singular dynamics of the nonlinear Schrödinger equation on a plane domain, Geom. Funct. Anal.13 (2003) 1-19. Zbl1044.35084MR1978490
- [12] Burq N, Gérard P, Tzvetkov N, An example of singular dynamics for the nonlinear Schrödinger equation on bounded domains, in: Colombini F, Nishitani T (Eds.), Proceedings of the Conference on Hyperbolic PDEs and Related Topics, Cortona, 2002, submitted for publication. Zbl1210.35225MR2056842
- [13] Cazenave T, An introduction to nonlinear Schrödinger equations, second ed., Textos de Métodos Matemáticos26 (1993).
- [14] Constantin P, Saut J.C, Local smoothing properties of dispersive equations, J. Amer. Math. Soc.1 (1988) 413-439. Zbl0667.35061MR928265
- [15] Constantin P, Saut J.C, Local smoothing properties of Schrödinger equations, Indiana Univ. Math. J.38 (1989) 791-810. Zbl0712.35022MR1017334
- [16] Christ M, Kiselev A, Maximal functions associated to filtrations, J. Funct. Anal.179 (2001) 409-425. Zbl0974.47025MR1809116
- [17] Doi S.I, Smoothing effects of Schrödinger evolution groups on Riemannian manifolds, Duke Math. J.82 (1996) 679-706. Zbl0870.58101MR1387689
- [18] Kato T, On nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Phys. Théor.46 (1987) 113-129. Zbl0632.35038MR877998
- [19] Kavian O, A remark on the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations, Trans. Amer. Math. Soc.299 (1987) 193-203. Zbl0638.35043MR869407
- [20] S. Keraani, Étude de quelques régimes asymptotiques de l'équation de Schrödinger, PhD Thesis, Université de Paris-Sud, December 2000.
- [21] Lax P, Phillips R, Scattering Theory, Pure Appl. Math., vol. 26, Academic Press, 1989. Zbl0697.35004MR1037774
- [22] Lions J.-L, Quelques méthodes de résolution des équations aux dérivées partielles non linéaires, Dunod, Paris, 1969.
- [23] Melrose R.B, Sjöstrand J, Singularities of boundary value problems I, Comm. Pure Appl. Math.31 (1978) 593-617. Zbl0368.35020MR492794
- [24] Melrose R.B, Sjöstrand J, Singularities of boundary value problems II, Comm. Pure Appl. Math.35 (1982) 129-168. Zbl0546.35083MR644020
- [25] Ogawa T, Ozawa T, Trudinger type inequalities and uniqueness of weak solutions for the nonlinear Schrödinger equations, J. Math. Anal. Appl.155 (1991) 531-540. Zbl0733.35095MR1097298
- [26] Segal I, Nonlinear semi-groups, Ann. Math.78 (1963) 339-364. Zbl0204.16004MR152908
- [27] Sulem C, Sulem P.L, The Nonlinear Schrödinger Equation. Self-Focusing and Wave Collapse, Applied Mathematical Sciences, vol. 139, Springer-Verlag, New York, 1999. Zbl0928.35157MR1696311
- [28] Sjölin P, Regularity of solutions to Schrödinger equations, Duke Math. J.55 (1987) 699-715. Zbl0631.42010MR904948
- [29] Smith H, Sogge C, On the critical semilinear wave equation outside convex obstacles, J. Amer. Math. Soc.8 (1995) 879-916. Zbl0860.35081MR1308407
- [30] Staffilani G, Tataru D, Strichartz estimates for a Schrödinger operator with nonsmooth coefficients, Comm. Partial Differential Equations27 (2002) 1337-1372. Zbl1010.35015MR1924470
- [31] Taylor M, Partial Differential Equations, Applied Mathematical Sciences, vols. 115, 116, 117, Springer-Verlag, New York, 1996. Zbl0869.35003MR1395147
- [32] Tsutsumi M, On smooth solutions to the initial-boundary value problem for the nonlinear Schrödinger equation in two space dimensions, Nonlinear Anal.13 (1989) 1051-1056. Zbl0693.35133MR1013309
- [33] Tsutsumi M, On global solutions to the initial-boundary value problem for the nonlinear Schrödinger equation in exterior domains, Comm. Partial Differential Equations16 (1991) 885-907. Zbl0738.35093MR1116848
- [34] Tsutsumi Y, Global solutions of the nonlinear Schrödinger equation in exterior domains, Comm. Partial Differential Equations8 (1984) 1337-1374. Zbl0542.35027MR711442
- [35] Vainberg B.R, Asymptotic Methods in Equations of Mathematical Physics, Gordon and Breach, New York, 1988. Zbl0743.35001MR1054376
- [36] Vasy A, Zworski M, Semiclassical estimates in asymptotically euclidean scattering, Comm. Math. Phys.212 (2000) 205-217. Zbl0955.58023MR1764368
- [37] Vega L, Schrödinger equations: pointwise convergence to the initial data, Proc. Amer. Math. Soc.102 (1988) 874-878. Zbl0654.42014MR934859
- [38] Vladimirov M.V, On the solvability of mixed problem for a nonlinear equation of Schrödinger type, Soviet Math. Dokl.29 (1984) 281-284. Zbl0585.35019
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.