On the energy-critical fractional Sch\"odinger equation in the radial case

Preprint English OPEN
Guo, Zihua; Sire, Yannick; Wang, Yuzhao; Zhao, Lifeng;
(2013)
  • Subject: Mathematics - Analysis of PDEs
    arxiv: Mathematics::Spectral Theory | Mathematics::Analysis of PDEs

We consider the Cauchy problem for the energy-critical nonlinear Schr\"odinger equation with fractional Laplacian (fNLS) in the radial case. We obtain global well-posedness and scattering in the energy space in the defocusing case, and in the focusing case with energy b... View more
  • References (21)
    21 references, page 1 of 3

    [1] T. Cazenave, F. Weissler, The Cauchy problem for the critical nonlinear Schr¨odinger equation in Hs, Nonlinear Anal., Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, 14, 1990, 10, 807-836

    [2] W. Chen, C. Li, B. Ou, Classification of solutions for an integral equation, Comm. Pure Appl. Math. , 59 (2006), 330-343.

    [3] Y. Cho, G. Hwang, S. Kwon, S. Lee, On the finite time blowup for mass-critical Hartree equations, arXiv:1208.2302.

    [4] Y. Cho, H. Hajaiej, G. Hwang, and T. Ozawa, On the Cauchy problem of fractional Schr¨odinger equation with Hartree type nonlinearity, arXiv:1209.5899.

    [5] Y. Cho, H. Hajaiej, G. Hwang, and T. Ozawa, On the orbital stability of fractional Schr¨odinger equations, arXiv:1302.2719.

    [6] Y. Cho, G. Hwang, S. Kwon, S. Lee, Profile decompositions and Blowup phenomena of mass critical fractional Schr¨odinger equations, arXiv:1208.2303.

    [7] Y. Cho, S. Lee, Strichartz Estimates in Spherical Coordinates, to appear in Indi. Univ. Math. J., arXiv:1202.3543v2.

    [8] A. Cotsiolis, N. K. Tavoularis, Best constants for Sobolev inequalities for higher order fractional derivatives, J. Math. Anal. Appl., 295 (2004), 225-236.

    [9] B. Guo, Y. Han, J. Xin, Existence of the global smooth solution to the period boundary value problem of fractional nonlinear Schr¨odinger equation. Appl. Math. Comput. 204, No 1 (2008), 468-477.

    [10] B. Guo and D. Huang, Existence and stability of standing waves for nonlinear fractional Schr¨odinger equations, J. Math. Phys. 53, 083702 (2012).

  • Metrics
    No metrics available
Share - Bookmark