메뉴 건너뛰기




Volumn 2005, Issue , 2005, Pages

Stability of energy-critical nonlinear Schrödinger equations in high dimensions

Author keywords

Local well posedness; Scattering theory; Strichartz estimates; Uniform well posedness

Indexed keywords


EID: 27644461939     PISSN: 10726691     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review
Times cited : (99)

References (21)
  • 1
    • 0040248890 scopus 로고    scopus 로고
    • Global well-posedness of defocusing 3D critical NLS in the radial case
    • J. Bourgain, Global well-posedness of defocusing 3D critical NLS in the radial case, JAMS 12 (1999), 145-171.
    • (1999) JAMS , vol.12 , pp. 145-171
    • Bourgain, J.1
  • 3
    • 0011576999 scopus 로고
    • Some remarks on the nonlinear Schrödinger equation in the critical case
    • Nonlinear semigroups, Partial Differential Equations and Attractors
    • T. Cazenave, F.B. Weissler, Some remarks on the nonlinear Schrödinger equation in the critical case, Nonlinear semigroups, Partial Differential Equations and Attractors, Lecture Notes in Math. 1394 (1989), 18-29.
    • (1989) Lecture Notes in Math. , vol.1394 , pp. 18-29
    • Cazenave, T.1    Weissler, F.B.2
  • 4
    • 23244446904 scopus 로고
    • Critical nonlinear Schrödinger Equation
    • T. Cazenave, F.B. Weissler, Critical nonlinear Schrödinger Equation, Non. Anal. TMA 14 (1990), 807-836.
    • (1990) Non. Anal. TMA , vol.14 , pp. 807-836
    • Cazenave, T.1    Weissler, F.B.2
  • 5
    • 2942580503 scopus 로고    scopus 로고
    • An introduction to nonlinear Schrödinger equations
    • Instituto de Matemática UFRJ
    • T. Cazenave, An introduction to nonlinear Schrödinger equations, Textos de Métodos Matemáticos 26, Instituto de Matemática UFRJ, 1996.
    • (1996) Textos de Métodos Matemáticos , vol.26
    • Cazenave, T.1
  • 6
    • 5444256656 scopus 로고    scopus 로고
    • Semilinear Schrödinger equations
    • American Mathematical Society
    • T. Cazenave, Semilinear Schrödinger equations, Courant Lecture Notes in Mathematics, 10. American Mathematical Society, 2003.
    • (2003) Courant Lecture Notes in Mathematics , vol.10
    • Cazenave, T.1
  • 11
    • 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. Poincare' Anal. Non Line'aire 2 (1985),309-327.
    • (1985) Ann. Inst. H. Poincare' Anal. Non Line'aire , vol.2 , pp. 309-327
    • Ginibre, J.1    Velo, G.2
  • 12
    • 36749114276 scopus 로고
    • On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger operators
    • R.T. Glassey, On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger operators, J. Math. Phys. 8 (1977), 1794-1797.
    • (1977) J. Math. Phys. , vol.8 , pp. 1794-1797
    • Glassey, R.T.1
  • 13
    • 0034353902 scopus 로고    scopus 로고
    • On nonlinear Schrödinger equations
    • M. Grillakis, On nonlinear Schrödinger equations, Comm. Partial Differential Equations 25 (2000), no. 9-10, 1827-1844.
    • (2000) Comm. Partial Differential Equations , vol.25 , Issue.9-10 , pp. 1827-1844
    • Grillakis, M.1
  • 14
    • 0001404168 scopus 로고
    • On nonlinear Schrödinger equations
    • T. Kato, On nonlinear Schrödinger equations, Ann. Inst. H. Poincare Phys. Theor. 46 (1987), 113-129.
    • (1987) Ann. Inst. H. Poincare Phys. Theor. , vol.46 , pp. 113-129
    • Kato, T.1
  • 15
    • 51649139542 scopus 로고
    • s-solutions and unconditional well-posedness
    • s-solutions and unconditional well-posedness, J. d'Analyse. Math. 67, (1995), 281-306.
    • (1995) J. D'Analyse. Math. , vol.67 , pp. 281-306
    • Kato, T.1
  • 16
    • 0001138601 scopus 로고    scopus 로고
    • Endpoint Strichartz Estimates
    • M. Keel, T. Tao, Endpoint Strichartz Estimates, Amer. Math. J. 120 (1998), 955-980.
    • (1998) Amer. Math. J. , vol.120 , pp. 955-980
    • Keel, M.1    Tao, T.2
  • 17
    • 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. Diff. Eq. 175, (2001), 353-392.
    • (2001) J. Diff. Eq. , vol.175 , pp. 353-392
    • Keraani, S.1
  • 18
    • 0001962910 scopus 로고    scopus 로고
    • Scattering theory for nonlinear Klein-GOrdon equation with Sobolev critical power
    • K. Nakanishi, Scattering theory for nonlinear Klein-GOrdon equation with Sobolev critical power, IMRN 1 (1999), 31-60.
    • (1999) IMRN , vol.1 , pp. 31-60
    • Nakanishi, K.1
  • 20
    • 27644533326 scopus 로고    scopus 로고
    • Global well-posedness and scattering for the higher-dimensional energy-critical nonlinear Schrödinger equation for radial data
    • to appear
    • T. Tao, Global well-posedness and scattering for the higher-dimensional energy-critical nonlinear Schrödinger equation for radial data, to appear New York Journal of Math.
    • New York Journal of Math.
    • Tao, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.