Table of Contents Author Guidelines Submit a Manuscript
Journal of Function Spaces and Applications
Volume 2013, Article ID 968603, 13 pages
http://dx.doi.org/10.1155/2013/968603
Research Article

Energy Scattering for Schrödinger Equation with Exponential Nonlinearity in Two Dimensions

School of Mathematical Sciences, Peking University, Beijing 100871, China

Received 9 January 2013; Accepted 24 February 2013

Academic Editor: Baoxiang Wang

Copyright © 2013 Shuxia Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Nakamura and T. Ozawa, “Nonlinear Schrödinger equations in the Sobolev space of critical order,” Journal of Functional Analysis, vol. 155, no. 2, pp. 364–380, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. B. X. Wang, “The smoothness of scattering operators for sinh-Gordon and nonlinear Schrödinger equations,” Acta Mathematica Sinica, vol. 18, no. 3, pp. 549–564, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. B. Wang, C. Hao, and H. Hudzik, “Energy scattering theory for the nonlinear Schrödinger equations with exponential growth in lower spatial dimensions,” Journal of Differential Equations, vol. 228, no. 1, pp. 311–338, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. S. Ibrahim, M. Majdoub, N. Masmoudi, and K. Nakanishi, “Scattering for the two-dimensional energy-critical wave equation,” Duke Mathematical Journal, vol. 150, no. 2, pp. 287–329, 2009. View at Google Scholar
  5. J. Colliander, S. Ibrahim, M. Majdoub, and N. Masmoudi, “Energy critical NLS in two space dimensions,” Journal of Hyperbolic Differential Equations, vol. 6, no. 3, pp. 549–575, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. K. Nakanishi, “Energy scattering for nonlinear Klein-Gordon and Schrödinger equations in spatial dimensions 1 and 2,” Journal of Functional Analysis, vol. 169, no. 1, pp. 201–225, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. R. Killip, T. Tao, and M. Visan, “The cubic nonlinear Schrödinger equation in two dimensions with radial data,” Journal of the European Mathematical Society, vol. 11, no. 6, pp. 1203–1258, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. B. Dodson, “Global well-posedness and scattering for the defocusing, L2-critical, nonlinear Schrödinger equation when d=2,” http://128.84.158.119/abs/1006.1375v1.
  9. C. E. Kenig and F. Merle, “Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrödinger equation in the radial case,” Inventiones Mathematicae, vol. 166, no. 3, pp. 645–675, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  10. S. Adachi and K. Tanaka, “Trudinger type inequalities in N and their best exponents,” Proceedings of the American Mathematical Society, vol. 128, no. 7, pp. 2051–2057, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J. Ginibre and G. Velo, “Scattering theory in the energy space for a class of nonlinear Schrödinger equations,” Journal de Mathématiques Pures et Appliquées, vol. 64, no. 4, pp. 363–401, 1985. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J. Bourgain, “Global well-posedness of defocusing 3D critical NLS in the radial case,” Journal of American Mathematical Society, vol. 12, pp. 145–171, 1999. View at Google Scholar
  13. T. Tao, M. Visan, and X. Zhang, “Minimal-mass blowup solutions of the mass-critical NLS,” Forum Mathematicum, vol. 20, no. 5, pp. 881–919, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. F. Merle and L. Vega, “Compactness at blow-up time for L2 solutions of the critical nonlinear Schrödinger equation in 2D,” International Mathematics Research Notices, no. 8, pp. 399–425, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. H. Bahouri and P. Gérard, “High frequency approximation of solutions to critical nonlinear wave equations,” American Journal of Mathematics, vol. 121, no. 1, pp. 131–175, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. P. Bégout and A. Vargas, “Mass concentration phenomena for the L2-critical nonlinear Schrödinger equation,” Transactions of the American Mathematical Society, vol. 359, no. 11, pp. 5257–5282, 2007. View at Publisher · View at Google Scholar · View at MathSciNet