Blow up of the critical norm for some radial L2 super critical nonlinear Schrödinger equations

American Journal of Mathematics

Volumn 130, Issue 4, 2008, Pages 945-978

  Merle, Frank ^a   Raphaël, Pierre ^b  

^a UNIVERSITÉ DE CERGY PONTOISE   (France)

^b UNIVERSITÉ PARIS SUD   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 50049127248     PISSN: 00029327     EISSN: None     Source Type: Journal    
DOI: 10.1353/ajm.0.0012     Document Type: Article

References (19)

1. Th. Cazenave, Semilinear Schrödinger Equations, Courant Lect. Notes Math., vol. 10, NYU, CIMS, AMS, 2003.
2. Th. Cazenave and F. Weissler, Some remarks on the nonlinear Schrödinger equation in the critical case, Nonlinear Semigroups, Partial Differential Equations and Attractors (Washington, DC, 1987), Lecture Notes in Math., vol. 1394, Springer-Verlag, Berlin, 1989, pp. 18-29.
3. J. Colliander, S. Raynor, C. Sulem, and D. Wright, On blow up solutions to NLS with low regularity initial data, preprint.
4. 3,∞-solutions of Navier-Stokes equations and backward uniqueness, Uspekhi Mat. Nauk 58 (2003), no. 2 (350), 3-44; translation, Russian Math. Surveys 58 (2003), no. 2, 211-250.
5. J. Ginibre and G. Velo, On a class of nonlinear Schrödinger equations. I, The Cauchy problem, general case, J. Fund. Anal. 32 (1979), no. 1, 1-32.
6. 1 for nonlinear Schrödinger equation, prepublication, Univ. P. M. Curie, R95031.
7. T. J. Kaper and V. Rottschäfer, Blowup in the nonlinear Schrödinger equation near critical dimension, J. Math. Anal. Appl. 268 (2002), no. 2, 517-549.
8. 2-critical generalized KdV equation, J. Amer. Math. Soc. 15 (2002), no. 3, 617-664.
9. Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation, Ann. of Math. (2) 155 (2002), no. 1, 235-280.
10. 2 critical nonlinear Schrödinger equation. Invent. Math. 156 (2004), 565-672.
11. Blow up dynamic and upper bound on the blow up rate for critical nonlinear Schrödinger equation, Ann of Math. 161 (2005), no. 1, 157-222.
12. On one blow up point solutions to the critical non linear Schrödinger equation, J. Hyperbolic Differential Equations 2 (2005), no. 4, 919-962.
13. Sharp lower bound on the blow up rate for critical nonlinear Schrödinger equation, J. Amer. Math. Soc. 19 (2006), no. 1, 37-90.
14. 2 concentration of blow up solutions for the nonlinear Schrödinger equation with critical power nonlinearity, J. Differential Equations 84 (1990), 205-214.
15. 1 solution for the nonlinear Schrödinger equation, J. Differential Equations 92 (1991), no. 2, 317-330.
16. 2 supercritical nonlinear Schrödinger equation, Duke Math. J. 134 (2) (2006), 199-258.
17. R. S. Strichartz, Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations. Duke Math. J. 44 (1977), no. 3, 705-714.
18. C. Sulem and P. L. Sulem, The Nonlinear Schrödinger Equation. Self-focusing and Wave Collapse, Appl. Math. Sci.. vol. 139, Springer-Verlag, New York, 1999.
19. V. E. Zakharov and A. B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in non-linear media, Sov. Phys. JETP 34 (1972), 62-69.