메뉴 건너뛰기




Volumn 57, Issue 8, 2004, Pages 987-1014

Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on ℝ 3

Author keywords

[No Author keywords available]

Indexed keywords


EID: 3042638517     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/cpa.20029     Document Type: Article
Times cited : (196)

References (33)
  • 1
    • 0000193318 scopus 로고    scopus 로고
    • Refinements of Strichartz' inequality and applications to 2D-NLS with critical nonlinearity
    • Bourgain, J. Refinements of Strichartz' inequality and applications to 2D-NLS with critical nonlinearity. Internal Math. Res. Notices 1998, no. 5, 253-283.
    • Internal Math. Res. Notices , vol.1998 , Issue.5 , pp. 253-283
    • Bourgain, J.1
  • 2
    • 0000046869 scopus 로고    scopus 로고
    • Scattering in the energy space and below for 3D NLS
    • Bourgain, J. Scattering in the energy space and below for 3D NLS. J. Anal. Math. 75 (1998), 267-297.
    • (1998) J. Anal. Math. , vol.75 , pp. 267-297
    • Bourgain, J.1
  • 3
    • 84862385563 scopus 로고    scopus 로고
    • American Mathematical Society Colloquium Publications, 46. American Mathematical Society, Providence, R.I.
    • Bourgain, J. Global solutions of nonlinear Schrödinger equations. American Mathematical Society Colloquium Publications, 46. American Mathematical Society, Providence, R.I., 1999.
    • (1999) Global Solutions of Nonlinear Schrödinger Equations
    • Bourgain, J.1
  • 4
    • 0040248890 scopus 로고    scopus 로고
    • Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case
    • Bourgain, J. Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case. J. Amer. Math. Soc. 12 (1999), no. 1, 145-171.
    • (1999) J. Amer. Math. Soc. , vol.12 , Issue.1 , pp. 145-171
    • Bourgain, J.1
  • 5
    • 0141973496 scopus 로고    scopus 로고
    • Textos de Métodos Matemáticos, 22. Federal University of Rio De Janeiro, Instituto de Mathemática, Rio de Janeiro
    • Cazenave, T. An introduction to nonlinear Schrödinger equations. Textos de Métodos Matemáticos, 22. Federal University of Rio De Janeiro, Instituto de Mathemática, Rio de Janeiro, 1996.
    • (1996) An Introduction to Nonlinear Schrödinger Equations
    • Cazenave, T.1
  • 7
    • 0002645561 scopus 로고
    • Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation
    • Christ, F. M.; Weinstein, M. I. Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation. J. Funct. Anal. 100 (1991), no. 1, 87-109.
    • (1991) J. Funct. Anal. , vol.100 , Issue.1 , pp. 87-109
    • Christ, F.M.1    Weinstein, M.I.2
  • 8
    • 0001923237 scopus 로고
    • Au delà des opérateurs pseudo-différentiels
    • Société Mathématique de France, Paris
    • Coifman, R. R.; Meyer, Y. Au delà des opérateurs pseudo-différentiels. Astérisque 57. Société Mathématique de France, Paris, 1978.
    • (1978) Astérisque , vol.57
    • Coifman, R.R.1    Meyer, Y.2
  • 9
    • 0001072134 scopus 로고
    • Commutateurs d'intégrales singulières et opérateurs multilinéaires
    • Coifman, R.; Meyer, Y. Commutateurs d'intégrales singulières et opérateurs multilinéaires. Ann. Inst. Fourier (Grenoble) 28 (1978), no. 3, xi, 177-202.
    • (1978) Ann. Inst. Fourier (Grenoble) , vol.28 , Issue.3
    • Coifman, R.1    Meyer, Y.2
  • 12
    • 0036345464 scopus 로고    scopus 로고
    • Global well-posedness for Schrödinger equations with derivative
    • Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. Global well-posedness for Schrödinger equations with derivative. SIAM J. Math. Anal. 33 (2001), no. 3, 649-669.
    • (2001) SIAM J. Math. Anal. , vol.33 , Issue.3 , pp. 649-669
    • Colliander, J.1    Keel, M.2    Staffilani, G.3    Takaoka, H.4    Tao, T.5
  • 13
    • 0036771238 scopus 로고    scopus 로고
    • Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation
    • Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation. Math, Res. Lett. 9 (2002), no. 5-6, 659-682.
    • (2002) Math, Res. Lett. , vol.9 , Issue.5-6 , pp. 659-682
    • Colliander, J.1    Keel, M.2    Staffilani, G.3    Takaoka, H.4    Tao, T.5
  • 14
    • 0037287349 scopus 로고    scopus 로고
    • A refined global well-posedness result for Schrödinger equations with derivative
    • Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. A refined global well-posedness result for Schrödinger equations with derivative. SIAM J. Math. Anal. 34 (2002), no. 1, 64-86.
    • (2002) SIAM J. Math. Anal. , vol.34 , Issue.1 , pp. 64-86
    • Colliander, J.1    Keel, M.2    Staffilani, G.3    Takaoka, H.4    Tao, T.5
  • 16
    • 0038806261 scopus 로고    scopus 로고
    • Sharp global well-posedness for KdV and modified KdV on ℝ and script T sign
    • Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. Sharp global well-posedness for KdV and modified KdV on ℝ and script T sign. J. Amer. Math. Soc. 16 (2003), no. 3, 705-749.
    • (2003) J. Amer. Math. Soc. , vol.16 , Issue.3 , pp. 705-749
    • Colliander, J.1    Keel, M.2    Staffilani, G.3    Takaoka, H.4    Tao, T.5
  • 18
    • 0000555922 scopus 로고
    • Scattering theory in the energy space for a class of nonlinear Schrödinger equations
    • Ginibre, J.; Velo, G. Scattering theory in the energy space for a class of nonlinear Schrödinger equations. J. Math. Pures Appl. (9) 64 (1985), no. 4, 363-01.
    • (1985) J. Math. Pures Appl. (9) , vol.64 , Issue.4 , pp. 363-401
    • Ginibre, J.1    Velo, G.2
  • 19
    • 0001123370 scopus 로고
    • Smoothing properties and retarded estimates for some dispersive evolution equations
    • Ginibre, J.; Velo, G. Smoothing properties and retarded estimates for some dispersive evolution equations. Comm. Math. Phys. 144 (1992), no. 1, 163-188.
    • (1992) Comm. Math. Phys. , vol.144 , Issue.1 , pp. 163-188
    • Ginibre, J.1    Velo, G.2
  • 20
    • 84990617895 scopus 로고
    • Commutator estimates and the Euler and Navier-Stokes equations
    • Kato, T.; Ponce, G. Commutator estimates and the Euler and Navier-Stokes equations. Comm. Pure Appl. Math. 41 (1988), no. 7, 891-907.
    • (1988) Comm. Pure Appl. Math. , vol.41 , Issue.7 , pp. 891-907
    • Kato, T.1    Ponce, G.2
  • 22
    • 0001138601 scopus 로고    scopus 로고
    • Endpoint Strichartz estimates
    • Keel, M.; Tao, T. Endpoint Strichartz estimates. Amer. J. Math. 120 (1998), no. 5, 955-980.
    • (1998) Amer. J. Math. , vol.120 , Issue.5 , pp. 955-980
    • Keel, M.1    Tao, T.2
  • 24
    • 33645897344 scopus 로고    scopus 로고
    • Quadratic forms for the l-D semilinear Schrödinger equation
    • Kenig, C. E.; Ponce, G.; Vega, L. Quadratic forms for the l-D semilinear Schrödinger equation. Trans. Amer. Math. Soc. 348 (1996), no. 8, 3323-3353.
    • (1996) Trans. Amer. Math. Soc. , vol.348 , Issue.8 , pp. 3323-3353
    • Kenig, C.E.1    Ponce, G.2    Vega, L.3
  • 25
    • 0000320001 scopus 로고
    • Decay and scattering of solutions of a nonlinear Schrödinger equation
    • Lin, J. E.; Strauss, W. A. Decay and scattering of solutions of a nonlinear Schrödinger equation. J. Funct. Anal. 30 (1978), no. 2, 245-263.
    • (1978) J. Funct. Anal. , vol.30 , Issue.2 , pp. 245-263
    • Lin, J.E.1    Strauss, W.A.2
  • 26
    • 0000408939 scopus 로고
    • Time decay for the nonlinear Klein-Gordon equations
    • Morawetz, C. S. Time decay for the nonlinear Klein-Gordon equations. Proc. Roy. Soc. Ser. A 306 (1968), 291-296.
    • (1968) Proc. Roy. Soc. Ser. A , vol.306 , pp. 291-296
    • Morawetz, C.S.1
  • 27
    • 0000617504 scopus 로고
    • Space-time decay for solutions of wave equations
    • Segal, I. Space-time decay for solutions of wave equations. Advances in Math. 22 (1976), no. 3, 305-311.
    • (1976) Advances in Math. , vol.22 , Issue.3 , pp. 305-311
    • Segal, I.1
  • 28
    • 84972553620 scopus 로고
    • Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
    • Strichartz, R. S. Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations. Duke Math. J. 44 (1977), no. 3, 705-714.
    • (1977) Duke Math. J. , vol.44 , Issue.3 , pp. 705-714
    • Strichartz, R.S.1
  • 29
    • 3042637188 scopus 로고
    • CBMS Regional Conference Series in Mathematics, 73. American Mathematical Society, Providence, R.I.
    • Strauss, W. Nonlinear wave equations. CBMS Regional Conference Series in Mathematics, 73. American Mathematical Society, Providence, R.I., 1989.
    • (1989) Nonlinear Wave Equations
    • Strauss, W.1
  • 30
    • 0035541508 scopus 로고    scopus 로고
    • Global regularity of wave maps. II. Small energy in two dimensions
    • Tao, T. Global regularity of wave maps. II. Small energy in two dimensions. Comm. Math, Phys. 224(2001), no. 2, 443-544.
    • (2001) Comm. Math, Phys. , vol.224 , Issue.2 , pp. 443-544
    • Tao, T.1
  • 31
    • 0035486554 scopus 로고    scopus 로고
    • 2 -functions, and applications to nonlinear dispersive equations
    • 2 -functions, and applications to nonlinear dispersive equations. Amer. J. Math. 123 (2001), no. 5, 839-908.
    • (2001) Amer. J. Math. , vol.123 , Issue.5 , pp. 839-908
    • Tao, T.1
  • 32
    • 0038161288 scopus 로고    scopus 로고
    • Pseudodifferential operators, paradifferential operators, and layer potentials. Mathematical Surveys and Monographs, 81. American Mathematical Society, Providence, R.I.
    • Taylor, M. E. Tools for PDE. Pseudodifferential operators, paradifferential operators, and layer potentials. Mathematical Surveys and Monographs, 81. American Mathematical Society, Providence, R.I., 2000.
    • (2000) Tools for PDE
    • Taylor, M.E.1
  • 33
    • 0000483491 scopus 로고
    • Existence of solutions for Schrödinger evolution equations
    • Yajima, K. Existence of solutions for Schrödinger evolution equations. Comm. Math. Phys. 110 (1987), no. 3, 415-426.
    • (1987) Comm. Math. Phys. , vol.110 , Issue.3 , pp. 415-426
    • Yajima, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.