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

*Guo, Zihua*;

*Sire, Yannick*;

*Wang, Yuzhao*;

*Zhao, Lifeng*;

- Subject: Mathematics - Analysis of PDEsarxiv: Mathematics::Spectral Theory | Mathematics::Analysis of PDEs

- References (21)
[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).

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