A priori bounds for the 1D cubic NLS in negative sobolev spaces

International Mathematics Research Notices

Volumn 2007, Issue , 2007, Pages

  Koch, Herbert ^a   Tataru, Daniel ^b  

^a UNIVERSITY OF BONN   (Germany)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 63449137936     PISSN: 10737928     EISSN: 16870247     Source Type: Journal    
DOI: 10.1093/imrn/rnm053     Document Type: Article

References (10)

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2. Christ, M., J. Colliander, and T. Tao. "A Priori Bounds and Weak Solutions for the Nonlinear Schr ̈ odinger Equation in Sobolev Spaces of Negative Order." (2006): Preprint arXiv:math.AP/0612457.
3. Christ, M., J. Colliander, and T. Tao. "Asymptotics, FrequencyModulation, and Low Regularity Ill-Posedness for Canonical Defocusing Equations." American Journal of Mathematics 125 (2003): 1235-1293.
4. Grünrock, A. "Bi- and Trilinear Schrö dinger Estimates in One Space Dimension with Applications to Cubic NLS and DNLS." International Mathematics Research Notices 41 (2005): 2525-2558.
5. Kappeler, T., and P. Topalov. "GlobalWell-Posedness of mKdV in L2(T,ℝ)." Communications in Partial Differential Equations 30 (2005): 435-449.
6. Kenig, C. E., G. Ponce, and L. Vega. "On the Ill-Posedness of Some Canonical Dispersive Equations." Duke Mathematical Journal 106 (2001): 617-633.
7. Koch, H., and D. Tataru. "Dispersive Estimates for Principally Normal Pseudodifferential Operators." Communications on Pure and Applied Mathematics 58 (2005): 217-284.
8. Smith, H., and C. Sogge. "On the lp Norm of Spectral Clusters for Compact Manifolds with Boundary." (2006): Preprint arXiv:math.AP/0605682.
9. Tao, T. Nonlinear Dispersive Equations, Volume 106 of CBMS Regional Conference Series in Mathematics. Washington, DC: Conference Board of the Mathematical Sciences, Local and Global Analysis, 2006.
10. Vargas, A., and L. Vega. "Global Wellposedness for 1D Non-Linear Schrödinger Equation for Data with An Infinite L2 Norm." Journal De Mathematiques Pures Et Appliquees (9) 80 (2001): 1029-1044.