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

作者: Yannick Sire , Zihua Guo , Yuzhao Wang , Lifeng Zhao

DOI:

关键词:

摘要: We consider the Cauchy problem for energy-critical nonlinear Schr\"odinger equation with fractional Laplacian (fNLS) in radial case. obtain global well-posedness and scattering energy space defocusing case, focusing case below ground state.

参考文章(15)
Gyeongha Hwang, Soonsik Kwon, Yonggeun Cho, Sanghyuk Lee, On finite time blowup for mass-critical Hartree equations arXiv: Analysis of PDEs. ,(2012)
Monica Visan, Terence Tao, STABILITY OF ENERGY-CRITICAL NONLINEAR SCHR¨ ODINGER EQUATIONS IN HIGH DIMENSIONS arXiv: Analysis of PDEs. ,(2005)
Elliott H. Lieb, Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities Annals of Mathematics. ,vol. 118, pp. 529- 554 ,(1983) , 10.1007/978-3-642-55925-9_43
Athanase Cotsiolis, Nikolaos K. Tavoularis, Best constants for Sobolev inequalities for higher order fractional derivatives Journal of Mathematical Analysis and Applications. ,vol. 295, pp. 225- 236 ,(2004) , 10.1016/J.JMAA.2004.03.034
Yonggeun Cho, Hichem Hajaiej, Gyeongha Hwang, Tohru Ozawa, On the Cauchy Problem of Fractional Schrödinger Equation with Hartree Type Nonlinearity Funkcialaj Ekvacioj. ,vol. 56, pp. 193- 224 ,(2013) , 10.1619/FESI.56.193
Yuqin Ke, Remark on the Strichartz estimates in the radial case Journal of Mathematical Analysis and Applications. ,vol. 387, pp. 857- 861 ,(2012) , 10.1016/J.JMAA.2011.09.039
Yonggeun Cho, Sanghyuk Lee, Strichartz Estimates in Spherical Coordinates arXiv: Analysis of PDEs. ,(2012)
Thierry Cazenave, Fred B. Weissler, The Cauchy problem for the critical nonlinear Schro¨dinger equation in H s Nonlinear Analysis-theory Methods & Applications. ,vol. 14, pp. 807- 836 ,(1990) , 10.1016/0362-546X(90)90023-A
Gyeongha Hwang, Soonsik Kwon, Yonggeun Cho, Sanghyuk Lee, Profile decompositions and Blowup phenomena of mass critical fractional Schr\"odinger equations arXiv: Analysis of PDEs. ,(2012)