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Volumn 18, Issue 6, 2009, Pages 1787-1840

Dynamic of threshold solutions for energy-critical NlS

Author keywords

Asymptotic behavior; Blow up; Energy critical; Nonlinear wave equation; Scattering

Indexed keywords


EID: 63949086654     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00039-009-0707-x     Document Type: Article
Times cited : (130)

References (20)
  • 1
    • 0001596880 scopus 로고
    • Équations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire.
    • T. AUBIN, Équations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire. J. Math. Pures Appl. (9) 55:3 (1976), 269-296.
    • (1976) J. Math. Pures Appl. (9) , vol.55 , Issue.3 , pp. 269-296
    • AUBIN, T.1
  • 3
    • 0040248890 scopus 로고    scopus 로고
    • Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case
    • J. BOURGAIN, Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case. J. Amer. Math. Soc. 12:1 (1999), 145-171.
    • (1999) J. Amer. Math. Soc , vol.12 , Issue.1 , pp. 145-171
    • BOURGAIN, J.1
  • 6
    • 85050669204 scopus 로고
    • The global Cauchy problem for the nonlinear Schrödinger equation revisited
    • J. GINIBRE, G. VELO, The global Cauchy problem for the nonlinear Schrödinger equation revisited, Ann. Inst. H. Poincaré Anal. Non Linéaire 2:4 (1985), 309-327.
    • (1985) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.2 , Issue.4 , pp. 309-327
    • GINIBRE, J.1    VELO, G.2
  • 7
    • 84990563336 scopus 로고
    • Analysis of the linearization around a critical point of an infinite-dimensional Hamiltonian system
    • M. GRILLAKIS, Analysis of the linearization around a critical point of an infinite-dimensional Hamiltonian system, Comm. Pure Appl. Math. 43:3 (1990), 299-333.
    • (1990) Comm. Pure Appl. Math , vol.43 , Issue.3 , pp. 299-333
    • GRILLAKIS, M.1
  • 8
    • 0001138601 scopus 로고    scopus 로고
    • Endpoint Strichartz estimates
    • M. KEEL, T. TAO, Endpoint Strichartz estimates, Amer. J. Math. 120:5 (1998), 955-980.
    • (1998) Amer. J. Math , vol.120 , Issue.5 , pp. 955-980
    • KEEL, M.1    TAO, T.2
  • 10
    • 0035922239 scopus 로고    scopus 로고
    • On the defect of compactness for the Strichartz estimates of the Schrödinger equations
    • S. KERAANI, On the defect of compactness for the Strichartz estimates of the Schrödinger equations, J. Differential Equations 175:2 (2001), 353-392.
    • (2001) J. Differential Equations , vol.175 , Issue.2 , pp. 353-392
    • KERAANI, S.1
  • 11
    • 34250849129 scopus 로고    scopus 로고
    • On the focusing critical semi-linear wave equation
    • J. KRIEGER, W. SCHLAG, On the focusing critical semi-linear wave equation, Amer. J. Math. 129:3 (2007), 843-913.
    • (2007) Amer. J. Math , vol.129 , Issue.3 , pp. 843-913
    • KRIEGER, J.1    SCHLAG, W.2
  • 12
    • 0001294182 scopus 로고
    • The concentration-compactness principle in the calculus of variations. The limit case. II
    • P.-L. LIONS, The concentration-compactness principle in the calculus of variations. The limit case. II, Rev. Mat. Iberoamericana 1:2 (1985), 45-121.
    • (1985) Rev. Mat. Iberoamericana , vol.1 , Issue.2 , pp. 45-121
    • LIONS, P.-L.1
  • 13
    • 84974001368 scopus 로고
    • Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power
    • F. MERLE, Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power, Duke Math. J. 69:2 (1993), 427-454.
    • (1993) Duke Math. J , vol.69 , Issue.2 , pp. 427-454
    • MERLE, F.1
  • 14
    • 0002944738 scopus 로고
    • The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent
    • O. REY, The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent, J. Funct. Anal. 89:1 (1990), 1-52.
    • (1990) J. Funct. Anal , vol.89 , Issue.1 , pp. 1-52
    • REY, O.1
  • 15
    • 33750419023 scopus 로고    scopus 로고
    • Spectral theory and nonlinear partial differential equations: A survey
    • W. SCHLAG, Spectral theory and nonlinear partial differential equations: a survey, Discrete Contin. Dyn. Syst. 15:3 (2006), 703-723.
    • (2006) Discrete Contin. Dyn. Syst , vol.15 , Issue.3 , pp. 703-723
    • SCHLAG, W.1
  • 16
    • 0000540347 scopus 로고
    • Existence of solitary waves in higher dimensions
    • W. A. STRAUSS, Existence of solitary waves in higher dimensions, Comm. Math. Phys. 55:2 (1977), 149-162.
    • (1977) Comm. Math. Phys , vol.55 , Issue.2 , pp. 149-162
    • STRAUSS, W.A.1
  • 17
    • 84972553620 scopus 로고
    • Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
    • R.S. STRICHARTZ, Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J. 44:3 (1977), 705-714.
    • (1977) Duke Math. J , vol.44 , Issue.3 , pp. 705-714
    • STRICHARTZ, R.S.1
  • 18
    • 34250392866 scopus 로고
    • Best constant in Sobolev inequality
    • G. TALENTI, Best constant in Sobolev inequality, Ann. Mat. Pura Appl. (4), 110 (1976), 353-372.
    • (1976) Ann. Mat. Pura Appl. (4) , vol.110 , pp. 353-372
    • TALENTI, G.1
  • 19
    • 27644461939 scopus 로고    scopus 로고
    • Stability of energy-critical nonlinear Schrödinger equations in high dimensions
    • 28pp
    • T. TAO, M. VISAN, Stability of energy-critical nonlinear Schrödinger equations in high dimensions, Electron. J. Differential Equations 118 (2005), 28pp.
    • (2005) Electron. J. Differential Equations , vol.118
    • TAO, T.1    VISAN, M.2
  • 20
    • 0003276928 scopus 로고
    • Linear Operators in Hilbert Spaces
    • translated from the German by Joseph Szücs, Springer-Verlag, New York
    • J. WEIDMANN, Linear Operators in Hilbert Spaces, (translated from the German by Joseph Szücs), Graduate Texts in Mathematics 68, Springer-Verlag, New York, 1980.
    • (1980) Graduate Texts in Mathematics , vol.68
    • WEIDMANN, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.