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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Energy-critical NLS with potentials of quadratic growth
Pages: 563 - 587, Issue 2, February 2018

doi:10.3934/dcds.2018025      Abstract        References        Full text (538.9K)           Related Articles

Casey Jao - Department of Mathematics, UC Berkeley, Berkeley, CA 94720, United States (email)

1 K. Asada and D. Fujiwara, On some oscillatory integral transformations in $L^{2}(R^n)$, Japan. J. Math. (N.S.), 4 (1978), 299-361.       
2 J. Bourgain, Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case, J. Amer. Math. Soc., 12 (1999), 145-171.       
3 H. Brézis and E. Lieb, A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer. Math. Soc., 88 (1983), 486-490.       
4 R. Carles, Nonlinear schrödinger equation with time-dependent potential, Commun. Math Sci., 9 (2011), 937-964.       
5 J. Colliander, M. Keel, G. Staffilani, H. Takaoka and T. Tao, Global well-posedness and scattering for the energy-critical nonlinear Schrödinger equation in $\mathbbR^3$, Ann. of Math. (2), 167 (2008), 767-865.       
6 G. B. Folland, Harmonic Analysis in Phase Space, vol. 122 of Annals of Mathematics Studies, Princeton University Press, Princeton, NJ, 1989.       
7 D. Fujiwara, On the boundedness of integral transformations with highly oscillatory kernels, Proc. Japan Acad., 51 (1975), 96-99.       
8 D. Fujiwara, A construction of the fundamental solution for the Schrödinger equation, J. Analyse Math., 35 (1979), 41-96.       
9 D. Fujiwara, Remarks on convergence of the Feynman path integrals, Duke Math. J., 47 (1980), 559-600.       
10 W. Hebisch, A multiplier theorem for Schrödinger operators, Colloq. Math., 60/61 (1990), 659-664.       
11 A. D. Ionescu and B. Pausader, The energy-critical defocusing NLS on $\mathbbT^3$, Duke Math. J., 161 (2012), 1581-1612.       
12 A. D. Ionescu and B. Pausader, Global well-posedness of the energy-critical defocusing NLS on $\mathbbR\times \mathbbT^3$, Comm. Math. Phys., 312 (2012), 781-831.       
13 A. D. Ionescu, B. Pausader and G. Staffilani, On the global well-posedness of energy-critical Schrödinger equations in curved spaces, Anal. PDE, 5 (2012), 705-746.       
14 C. Jao, The energy-critical quantum harmonic oscillator, Comm. Partial Differential Equations, 41 (2016), 79-133.       
15 M. Keel and T. Tao, Endpoint Strichartz estimates, Amer. J. Math., 120 (1998), 955-980.       
16 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, Invent. Math., 166 (2006), 645-675.       
17 S. Keraani, On the blow up phenomenon of the critical nonlinear Schrödinger equation, J. Funct. Anal., 235 (2006), 171-192.       
18 R. Killip, S. Kwon, S. Shao and M. Visan, On the mass-critical generalized KdV equation, Discrete Contin. Dyn. Syst., 32 (2012), 191-221.       
19 R. Killip, B. Stovall and M. Visan, Scattering for the cubic Klein-Gordon equation in two space dimensions, Trans. Amer. Math. Soc., 364 (2012), 1571-1631.       
20 R. Killip and M. Visan, The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher, Amer. J. Math., 132 (2010), 361-424.       
21 R. Killip and M. Vişan, Nonlinear Schrödinger equations at critical regularity, in Evolution equations, vol. 17 of Clay Math. Proc., Amer. Math. Soc., Providence, RI, 2013, 325-437.       
22 R. Killip, M. Visan and X. Zhang, Quintic NLS in the exterior of a strictly convex obstacle, Amer. J. Math., 138 (2016), 1193-1346.       
23 R. Killip, M. Visan and X. Zhang, Energy-critical NLS with quadratic potentials, Comm. Partial Differential Equations, 34 (2009), 1531-1565.       
24 Y.-G. Oh, Cauchy problem and Ehrenfest's law of nonlinear Schrödinger equations with potentials, J. Differential Equations, 81 (1989), 255-274.       
25 E. Ryckman and M. Visan, Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in $\mathbbR^{1+4}$, Amer. J. Math., 129 (2007), 1-60.       
26 M. E. Taylor, Tools for PDE, vol. 81 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, 2000, Pseudodifferential operators, paradifferential operators, and layer potentials.       
27 M. Visan, The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions, Duke Math. J., 138 (2007), 281-374.       
28 J. Zhang, Stability of attractive Bose-Einstein condensates, J. Statist. Phys., 101 (2000), 731-746.       

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