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Book Information

Author(s): J. Bourgain
Title: Global solutions of nonlinear Schrödinger equations
Additional book information: Amer. Math. Soc., Providence, RI, 1999, viii+182, $35.00, 0-8218-1919-4

1.: J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations, Part I, Geom. Func. Anal. 3 (1993), 107-156. Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations, Part II, Geom. Func. Anal. 3 (1993), 209-262. MR 95d:35160a, MR 95d:35160b
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10.: J. Colliander, J. Delort, C. Kenig, G. Staffilani, Bilinear estimates and applications to 2D NLS, Trans. Amer. Math. Soc., 353 (2001), no. 8, 3307-3325. MR 2002d:35186
11.: J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Global well-posedness for Schrödinger equations with derivatives, SIAM J. Math. Anal. 3 (2001), 649-669.
12.: J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, A refined global well-posedness result for Schrödinger equations with derivatives, To appear in SIAM J. Math. Anal. (2002).
13.: J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Sharp global well-posedness for KdV and modified KdV on ${\mathbb R}$ and ${\mathbb T}$ , preprint (2002).
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22.: N. Katz, T. Tao, Bounds on arithmetic projections, and applications to the Kakeya conjecture, Math. Res. Lett. 6 (1999), no. 5-6, 625-630. MR 2000m:28006
23.: M. Keel, T. Tao, Endpoint Strichartz estimates, Amer. J. Math. 120(5) (1998), 955-980. MR 2000d:35018
24.: C.E. Kenig, G. Ponce, L. Vega, Oscillatory integrals and regularity of dispersive equations, Indiana Univ. Math. J. 40 (1991), 33-69. MR 92d:35081
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26.: C.E. Kenig, G. Ponce, L. Vega, Small solutions to nonlinear Schrödinger equations, Ann. Inst. Henri Poincaré 10 (1993), 255-288. MR 94h:35238
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32.: H. Lindblad, Sharp counterexample to the local existence of low-regularity solutions to nonlinear wave equations, Duke Math. J. 72 (1993), no. 2, 503-539. MR 94h:35165
33.: Y. Martel, F. Merle, A Liouville theorem for the critical generalized Korteweg-de Vries equation, J. Math. Pures Appl. 79(9) (2000), no. 4, 339-425. MR 2001i:37102
34.: Y. Martel, F. Merle, Asymptotic stability of solitons for subcritical generalized KdV equations, Arch. Ration. Mech. Anal. 157 (2001), no. 3, 219-254. CMP 2002:11
35.: Y. Martel, F. Merle, Instability of solitons for the critical generalized Korteweg-de Vries equation, Geom. Funct. Anal. 11 (2001), no. 1, 74-123. MR 2002g:35182
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49.: T. Wolff, A Kakeya-type problem for circles, Amer. J. Math. 119 (1997), no. 5, 985-1026. MR 98m:42027
50.: T. Wolff, Recent work connected with the Kakeya problem, Prospects in mathematics (Princeton, NJ, 1996), 129-162, Amer. Math. Soc., Providence, RI, 1999. MR 2000d:42010
51.: V.E. Zakharov, Collapse of Langmuir waves, Sov. Phys. JETP 35 (1997), 908-914.
52.: V.E. Zakharov, V.S. L'vov, G. Falkovich, Kolmogorov spectra of turbulence, Springer series in nonlinear dynamics, Berlin ; New York : Springer-Verlag, (1992).

Reviewer(s):
Gigliola Staffilani
Affiliation: Massachusetts Institute of Technology
Email: gigliola@math.mit.edu

MSC (2000): Primary 35Q55
DOI: 10.1090/S0273-0979-02-00956-4
PII: S 0273-0979(02)00956-4
Posted: October 16, 2002
Copyright of article: Copyright 2002, American Mathematical Society

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ISSN 1088-9485(e) ISSN 0273-0979(p)

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