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Volumn 161, Issue 1, 2005, Pages 157-222

The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation

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EID: 20444437961     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.4007/annals.2005.161.157     Document Type: Article
Times cited : (349)

References (30)
  • 1
    • 0020591567 scopus 로고
    • Nonlinear scalar field equations. I. Existence of a ground state
    • H. BERESTYCKI and P.-L. LIONS, Nonlinear scalar field equations. I. Existence of a ground state, Arch. Rational Mech. Anal. 82 (1983), 313-345.
    • (1983) Arch. Rational Mech. Anal. , vol.82 , pp. 313-345
    • Berestycki, H.1    Lions, P.-L.2
  • 3
    • 0002088365 scopus 로고
    • Harmonic analysis and nonlinear partial differential equations
    • (Zürich, 1994) Birkhäuser, Basel
    • _, Harmonic analysis and nonlinear partial differential equations, Proc. Internat. Congress of Mathematicians (Zürich, 1994) 1, 2, 31-44, Birkhäuser, Basel, 1995.
    • (1995) Proc. Internat. Congress of Mathematicians , vol.1 , Issue.2 , pp. 31-44
  • 4
    • 0000246714 scopus 로고    scopus 로고
    • Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity
    • J. BOURGAIN and W. WANG, Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 25 (1997), 197-215, no. 1-2, 1998.
    • (1997) Ann. Scuola Norm. Sup. Pisa Cl. Sci. , vol.25 , Issue.1-2 , pp. 197-215
    • Bourgain, J.1    Wang, W.2
  • 5
    • 0011576999 scopus 로고
    • Some remarks on the nonlinear Schrödinger equation in the critical case. Nonlinear semigroups, partial differential equations and attractors
    • (Washington, DC, 1987), Springer-Verlag, New York
    • TH. CAZENAVE and F. WEISSLER, Some remarks on the nonlinear Schrödinger equation in the critical case. Nonlinear semigroups, partial differential equations and attractors (Washington, DC, 1987), 18-29, Lecture Notes in Math. 1394, Springer-Verlag, New York, 1989.
    • (1989) Lecture Notes in Math. , vol.1394 , pp. 18-29
    • Cazenave, Th.1    Weissler, F.2
  • 6
    • 0000256483 scopus 로고    scopus 로고
    • A modulation method for self-focusing in the perturbed critical nonlinear Schrödinger equation
    • G. FIBICH and G. PAPANICOLAOU, A modulation method for self-focusing in the perturbed critical nonlinear Schrödinger equation, Phys. Lett. A 239 (1998), 167-173.
    • (1998) Phys. Lett. A , vol.239 , pp. 167-173
    • Fibich, G.1    Papanicolaou, G.2
  • 7
    • 34250271532 scopus 로고
    • Symmetry and related properties via the maximum principle
    • B. GIDAS, W. M. Ni, and L. NIRENBERG, Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979), 209-243.
    • (1979) Comm. Math. Phys. , vol.68 , pp. 209-243
    • Gidas, B.1    Ni, W.M.2    Nirenberg, L.3
  • 8
    • 49249148441 scopus 로고
    • On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case
    • J. GINIBRE and G. VELO, On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case, J. Funct. Anal. 32 (1979), 1-32.
    • (1979) J. Funct. Anal. , vol.32 , pp. 1-32
    • Ginibre, J.1    Velo, G.2
  • 9
    • 21344478851 scopus 로고
    • Existence of self-similar blow-up solutions for Zakharov equation in dimension two. I
    • L. GLANGETAS and F. MERLE, Existence of self-similar blow-up solutions for Zakharov equation in dimension two. I, Comm. Math. Phys. 160 (1994), 173-215.
    • (1994) Comm. Math. Phys. , vol.160 , pp. 173-215
    • Glangetas, L.1    Merle, F.2
  • 10
  • 12
    • 0000893351 scopus 로고
    • Rate of blowup for solutions of the nonlinear Schrödinger equation at critical dimension
    • M. J. LANDMAN, G. C. PAPANICOLAOU, C. SULEM, and P.-L. SULEM, Rate of blowup for solutions of the nonlinear Schrödinger equation at critical dimension, Phys. Rev. A 38 (1988), 3837-3843.
    • (1988) Phys. Rev. A , vol.38 , pp. 3837-3843
    • Landman, M.J.1    Papanicolaou, G.C.2    Sulem, C.3    Sulem, P.-L.4
  • 13
    • 0034164847 scopus 로고    scopus 로고
    • A liouville theorem for the critical generalized Korteweg-de Vries equation
    • Y. MARTEL and F. MERLE, A liouville theorem for the critical generalized Korteweg-de Vries equation, J. de Math. Pures et Appl. 79 (2000), 339-425.
    • (2000) J. de Math. Pures et Appl. , vol.79 , pp. 339-425
    • Martel, Y.1    Merle, F.2
  • 14
    • 0036000529 scopus 로고    scopus 로고
    • Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation
    • _, Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation, Ann. of Math. 155 (2002), 235-280.
    • (2002) Ann. of Math. , vol.155 , pp. 235-280
  • 15
    • 0036016142 scopus 로고    scopus 로고
    • 2-critical generalized KdV equation
    • 2-critical generalized KdV equation, J. Amer. Math. Soc. 15 (2002), 617-664.
    • (2002) J. Amer. Math. Soc. , vol.15 , pp. 617-664
  • 16
    • 0035635809 scopus 로고    scopus 로고
    • Instability of solitons for the critical generalized Korteweg-de Vries equation
    • _, Instability of solitons for the critical generalized Korteweg-de Vries equation, Geom. Funct. Anal. 11 (2001), 74-123.
    • (2001) Geom. Funct. Anal. , vol.11 , pp. 74-123
  • 17
    • 0035616659 scopus 로고    scopus 로고
    • Existence of blow-up solutions in the energy space for the critical generalized KdV equation
    • F. MERLE, Existence of blow-up solutions in the energy space for the critical generalized KdV equation, J. Amer. Math. Soc. 14 (2001), 555-578.
    • (2001) J. Amer. Math. Soc. , vol.14 , pp. 555-578
    • Merle, F.1
  • 18
    • 0003278684 scopus 로고    scopus 로고
    • Blow-up phenomena for critical nonlinear Schrödinger and Zakharov equations
    • Proc. Internat. Congress of Mathematicians (Berlin, 1998) (Extra Vol. III)
    • _, Blow-up phenomena for critical nonlinear Schrödinger and Zakharov equations, Proc. Internat. Congress of Mathematicians (Berlin, 1998), Doc. Math 1998 (Extra Vol. III), 57-66.
    • Doc. Math , vol.1998 , pp. 57-66
  • 19
    • 84974001368 scopus 로고
    • Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power
    • _, Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power, Duke Math. J. 69 (1993), 427-454.
    • (1993) Duke Math. J. , vol.69 , pp. 427-454
  • 20
    • 0033484486 scopus 로고    scopus 로고
    • Asymptotic and limiting profiles of blowup solutions of the nonlinear Schrödinger equation with critical power
    • H. NAWA, Asymptotic and limiting profiles of blowup solutions of the nonlinear Schrödinger equation with critical power, Comm. Pure Appl. Math. 52 (1999), 193-270.
    • (1999) Comm. Pure Appl. Math. , vol.52 , pp. 193-270
    • Nawa, H.1
  • 21
    • 0000835523 scopus 로고
    • 1 solution for the nonlinear Schrödinger equation
    • 1 solution for the nonlinear Schrödinger equation, J. Differential Equations 92 (1991), 317-330.
    • (1991) J. Differential Equations , vol.92 , pp. 317-330
    • Ogawa, T.1    Tsutsumi, Y.2
  • 22
    • 0000028784 scopus 로고
    • Singular solutions of the Zakharov equations for Langmuir turbulence
    • G. C. PAPANICOLAOU, C. SULEM, P.-L. SULEM, and X. P. WANG, Singular solutions of the Zakharov equations for Langmuir turbulence, Phys. Fluids B 3 (1991), 969-980.
    • (1991) Phys. Fluids B , vol.3 , pp. 969-980
    • Papanicolaou, G.C.1    Sulem, C.2    Sulem, P.-L.3    Wang, X.P.4
  • 23
    • 0035537074 scopus 로고    scopus 로고
    • On the blow-up phenomenon for the critical nonlinear Schrödinger equation in 1D
    • G. PERELMAN, On the blow-up phenomenon for the critical nonlinear Schrödinger equation in 1D, Ann. Henri. Poincaré 2 (2001), 605-673.
    • (2001) Ann. Henri. Poincaré , vol.2 , pp. 605-673
    • Perelman, G.1
  • 24
    • 0033460613 scopus 로고    scopus 로고
    • Resonances, radiation damping and instability in Hamiltonian nonlinear wave equations
    • A. SOFFER and M. I. WEINSTEIN, Resonances, radiation damping and instability in Hamiltonian nonlinear wave equations, Invent. Math. 136 (1999), 9-74.
    • (1999) Invent. Math. , vol.136 , pp. 9-74
    • Soffer, A.1    Weinstein, M.I.2
  • 27
    • 84990553584 scopus 로고
    • Lyapunov stability of ground states of nonlinear dispersive evolution equations
    • M. I. WEINSTEIN, Lyapunov stability of ground states of nonlinear dispersive evolution equations, Comm. Pure. Appl. Math. 39 (1986), 51-68.
    • (1986) Comm. Pure. Appl. Math. , vol.39 , pp. 51-68
    • Weinstein, M.I.1
  • 28
    • 0000686130 scopus 로고
    • Modulational stability of ground states of nonlinear Schrödinger equations
    • _, Modulational stability of ground states of nonlinear Schrödinger equations, SIAM J. Math. Anal 16 (1985), 472-491.
    • (1985) SIAM J. Math. Anal , vol.16 , pp. 472-491
  • 29
    • 0041473959 scopus 로고
    • Nonlinear Schrödinger equations and sharp interpolation estimates
    • _, Nonlinear Schrödinger equations and sharp interpolation estimates, Comm. Math. Phys. 87 (1983), 567-576.
    • (1983) Comm. Math. Phys. , vol.87 , pp. 567-576
  • 30
    • 0002557939 scopus 로고
    • Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media
    • V. E. ZAKHAROV and A. B. SHABAT, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Sov. Phys. JETP 34 (1972), 62-69.
    • (1972) Sov. Phys. JETP , vol.34 , pp. 62-69
    • Zakharov, V.E.1    Shabat, A.B.2


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