Compactness at Blow-up Time for L2 Solutions of the Critical Nonlinear Schrödinger Equation in 2D

International Mathematics Research Notices

Volumn , Issue 8, 1998, Pages 398-425

  Merle, F ^a   Vega, L ^b  

^a UNIVERSITÉ DE CERGY PONTOISE   (France)

^b UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1842709141     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (10)

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2. J. Bourgain, "Some new estimates on oscillatory integrals" in Essays on Fourier Analysis in Honor of Elias M. Stein (Princeton, NJ, 1991), Princeton Math. Ser. 42, Princeton Univ. Press, Princeton, 1995, 83-112.
3. _, Refinements of Strichartz's inequality and applications to 2D-NLS with critical nonlinearity, IMRN (Internat. Math. Res. Notices) 1998, 253-283.
4. T. Cazenave, An Introduction to Nonlinear Schrödinger Equations, Text. Métod. Mat. 26, Univ. Fed. Rio de Janeiro, Rio de Janeiro, 1989.
5. T. Cazenave and F. Weissler, "Some remarks on the nonlinear Schrödinger equation in the critical case" in Nonlinear Semigroups, Partial Differential Equations and Attractors (Washington, DC, 1987), Lecture Notes in Math. 1394, Springer-Verlag, Berlin, 1989, 18-29.
6. P. Gerard, Description du défaut de compacité de l'injection de Sobolev, preprint.
7. F. Merle, Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power, Duke Math. J. 69 (1993), 427-454.
8. _, Lower bounds for the blow-up rate of solutions of the Zakharov equation in dimension two, Comm. Pure Appl. Math 49 (1996), 765-794.
9. 3, to appear in Duke Math. J.
10. R. Strichartz, Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math J. 44 (1977), 705-714.