Global well-posedness and polynomial bounds for the defocusing L 2-critical nonlinear Schrodinger equation in ℝ

Communications in Partial Differential Equations

Volumn 33, Issue 8, 2008, Pages 1395-1429

  De Silva, Daniela ^a   Pavlović, Nataša ^b   Staffilani, Gigliola ^c   Tzirakis, Nikolaos ^d  

^a JOHNS HOPKINS UNIVERSITY   (United States)

^b PRINCETON UNIVERSITY   (United States)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^d UNIVERSITY OF TORONTO   (Canada)

Author keywords

Global well posedness; Morawetz estimates; Schrodinger equation

Indexed keywords

EID: 49549105344     PISSN: 03605302     EISSN: 15324133     Source Type: Journal    
DOI: 10.1080/03605300701588839     Document Type: Article

References (25)

1. Bourgain, J. (1998). Refinements of Strichartz' inequality and applications to 2D-NLS with critical nonlinearity. International Mathematical Research Notices 5:253-283.
2. Bourgain, J. (1999). Global Solutions of Nonlinear Schrödinger Equations. Providence, RI: American Mathematical Society.
3. s. Nonlinear Analysis, Theory, Methods and Applications 14:807-836.
4. Cazenave, T. (2003). Semilinear Schrödinger Equations. CLN 10. Providence, RI: American Mathematical Society.
5. Coifman, R., Meyer, Y. (1978). Commutateurs d'intégrales singuliéres et opérateurs multilinéaires. Ann. Inst. Fouirer (Grenoble) 28:177-202.
6. 2. International Mathematical Research Notices 2007 2007:rnm090.
7. Colliander, J., Holmer, J., Visan, M., Zhang, X. (2008). Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on ℝ. Commun. Pure Appl. Anal. 7:467-489.
8. Colliander, J., Keel, M., Staffilani, G., Takaoka, H., Tao, T. (2001). Global well-posedness for Schrödinger equations with derivative. SIAM J. Math. Anal. 33:64-86.
9. Colliander, J., Keel, M., Staffilani, G., Takaoka, H., Tao, T. (2002). A refined global well-posedness result for Schrödinger equations with derivative. SIAM J. Math. Anal. 34(3):649-669.
10. Colliander, J., Keel, M., Staffilani, G., Takaoka, H., Tao, T. (2002). Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation. Math. Research Letters 9:659-682.
11. 3. CPAM 57:987-1014.
12. Colliander, J., Keel, M., Staffilani, G., Takaoka, H., Tao, T. (2006). Viriel, Morawetz and interaction Morawetz inequalities. Notes. Available at http://www.math.ucla.edu/tao/preprints/pde.html.
13. 3. To appear in Annals Math.
14. 2-critical nonlinear Schrödinger equation in higher dimensions. Commun. Pure Appl. Anal. 6:1023-1041.
15. 2+1. J. Hyperbolic Differ. Equ. 4:233-257.
16. Ginibre, J. (1996). Le probléme de Cauchy pour des EDP semi-linéaires périodiques en variables d'espace (d'aprés Bourgain). Astérique 237 (1996), Séminaire Bourbaki, Vol. 1994/1995, Exp. No. 796, 163-187.
17. Ginibre, J., Velo, G. (1985). The global Cauchy problem for the nonlinear Schrödinger equation. H. Poincaré Analyse Non Linéaire 2:309-327.
18. Kenig, C. E., Ponce, G., Vega, L. (1996). Quadratic forms for the 1-D semilinear Schrödinger equation. Trans. Amer. Math. Soc. 348:3323-3353.
19. Keel, M., Tao, T. (1998). Endpoint Strichartz estimates. H. Poincaré Analyse Non Linéaire 120:955-980.
20. Keel, M., Tao, T. Global well-posedness for large data for the Maxwell-Klein-Gordon equation below the energy norm. Preprint.
21. 1+1 for rough data. Intl. Math. Res. Notices 21:1117-1156.
22. Tao, T. (2006). Nonlinear dispersive equations. Local and global analysis. CBMS 106. Providence, RI: American Mathematical Society.
23. Tao, T., Visan, M., Zhang, X. Minimal-mass blowup solutions of the mass-critical NLS. To appear in Forum Mathematicum.
24. Tao, T., Visan, M., Zhang, X. (2007). Global well-posedness and scattering for the mass-critical nonlinear Schrödinger equations for radial data in high dimensions. Duke Math. J. 140:165-202.
25. Tzirakis, N. (2005). The Cauchy problem for the semi-linear quintic Schrödinger equation in 1D. Differential Integral Equations 18:947-960.