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Volumn 135, Issue 10, 2007, Pages 3255-3262

Rate of L2-concentration of blow-up solutions for critical nonlinear Schrödinger equation

Author keywords

Blow up; Critical nonlinear Schr dinger equation; Rate of L 2 concentration

Indexed keywords


EID: 67651231199     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-07-08902-2     Document Type: Article
Times cited : (3)

References (21)
  • 1
    • 0000246714 scopus 로고    scopus 로고
    • Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity
    • MR1655515 99m:35219
    • J. Bourgain and W. Wang, Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity, Ann. Sc. Norm. Super. Pisa Cl. Sci. 25 (1997), 197-215. MR1655515 (99m:35219)
    • (1997) Ann. Sc. Norm. Super. Pisa Cl. Sci. , vol.25 , pp. 197-215
    • Bourgain, J.1    Wang, W.2
  • 2
    • 0003197180 scopus 로고
    • An introduction to nonlinear Schrödinger equations
    • Rio de Janeiro
    • T. Cazenave, An introduction to nonlinear Schrödinger equations, Textos de metodos mathmatics, 22 Rio de Janeiro, 1989.
    • (1989) Textos de Metodos Mathmatics , vol.22
    • Cazenave, T.1
  • 3
    • 49249148441 scopus 로고
    • On a class of nonlinear Schrödinger equations
    • MR533219 82c:35058
    • J. Ginibre and G. Velo, On a class of nonlinear Schrödinger equations, J. Funct. Anal. 32 (1979), 1-71. MR533219 (82c:35058)
    • (1979) J. Funct. Anal. , vol.32 , pp. 1-71
    • Ginibre, J.1    Velo, G.2
  • 4
    • 36749114276 scopus 로고
    • On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations
    • MR0460850 57:842
    • R. T. Glassy, On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations, J. Math. Phys. 18 (1977), 1794-1797. MR0460850 (57:842)
    • (1977) J. Math. Phys. , vol.18 , pp. 1794-1797
    • Glassy, R.T.1
  • 6
    • 0000893351 scopus 로고
    • Rate of blowup for solutions of the nonlinear Schrödinger equation at critical dimension
    • MR966356 89k:35218
    • 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. MR966356 (89k:35218)
    • (1988) Phys. Rev. A , vol.38 , pp. 3837-3843
    • Landman, M.J.1    Papanicolaou, G.C.2    Sulem, C.3    Sulem, P.L.4
  • 7
    • 0041350485 scopus 로고    scopus 로고
    • Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation
    • MR1995801 2005j:35207
    • F. Merle and P. Raphaël, Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation, Geom. Funct. Anal. 13 (2003), 591-642. MR1995801 (2005j:35207)
    • (2003) Geom. Funct. Anal. , vol.13 , pp. 591-642
    • Merle, F.1    Raphaël, P.2
  • 8
    • 2942586742 scopus 로고    scopus 로고
    • 2 critical nonlinear Schrödinger equation
    • MR2061329 2006a:35283
    • 2 critical nonlinear Schrödinger equation, Invent. Math. 156 (2004), 565-672. MR2061329 (2006a:35283)
    • (2004) Invent. Math. , vol.156 , pp. 565-672
    • Merle, F.1    Raphaël, P.2
  • 9
    • 20444437961 scopus 로고    scopus 로고
    • The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation
    • MR2150386 2006k:35277
    • F. Merle and P. Raphaël, The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation, Annals of Math. (2) 161 (2005), 157-222. MR2150386 (2006k:35277)
    • (2005) Annals of Math. , vol.161 , Issue.2 , pp. 157-222
    • Merle, F.1    Raphaël, P.2
  • 10
    • 12444281836 scopus 로고    scopus 로고
    • Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation
    • MR2116733 2006m:35346
    • F. Merle and P. Raphaël, Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation, Comm. Math. Phys. 253 (2005), 675-704. MR2116733 (2006m:35346)
    • (2005) Comm. Math. Phys. , vol.253 , pp. 675-704
    • Merle, F.1    Raphaël, P.2
  • 11
    • 30644464564 scopus 로고    scopus 로고
    • 2 critical nonlinear Schrödinger equation
    • MR2169042 2006j:35223
    • 2 critical nonlinear Schrödinger equation, J. Amer. Soc. 19 (2005), 37-90. MR2169042 (2006j:35223)
    • (2005) J. Amer. Soc. , vol.19 , pp. 37-90
    • Merle, F.1    Raphaël, P.2
  • 12
    • 0000704928 scopus 로고
    • 2-concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity
    • MR1047566 91e:35194
    • 2-concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity. J. Diff. Eqs. 84 (1990), 205-214. MR1047566 (91e:35194)
    • (1990) J. Diff. Eqs. , vol.84 , pp. 205-214
    • Merle, F.1    Tsutsumi, Y.2
  • 13
    • 0033484486 scopus 로고    scopus 로고
    • Asymptotic and limiting profiles of blowup solutions of the nonlinear Schrödinger equation with critical power
    • MR1653454 99m:35235
    • 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. MR1653454 (99m:35235)
    • (1999) Comm. Pure Appl. Math. , vol.52 , pp. 193-270
    • Nawa, H.1
  • 14
    • 0035537074 scopus 로고    scopus 로고
    • On the blow-up phenomenon for the critical nonlinear Schrödinger equation in 1D
    • G. C. 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.C.1
  • 15
    • 13844296411 scopus 로고    scopus 로고
    • Stability of log-log bound for blow up solutions to the critical nonlinear Schrödinger equation
    • MR2122541 2006b:35303
    • P. Raphaël, Stability of log-log bound for blow up solutions to the critical nonlinear Schrödinger equation, Math. Ann. 331 (2005), 577-609. MR2122541 (2006b:35303)
    • (2005) Math. Ann. , vol.331 , pp. 577-609
    • Raphaël, P.1
  • 16
    • 0000835523 scopus 로고
    • 1 solution for the nonlinear Schrödinger equation
    • MR1120908 92k:35262
    • 1 solution for the nonlinear Schrödinger equation, J. Diff. Eq. 92 (1991), 317-330. MR1120908 (92k:35262)
    • (1991) J. Diff. Eq. , vol.92 , pp. 317-330
    • Ogawa, T.1    Tsutsumi, Y.2
  • 17
    • 84968486052 scopus 로고
    • 1 solution for the nonlinear Schrödinger equation with critical power nonlinearity
    • MR1045145 91f:35026
    • 1 solution for the nonlinear Schrödinger equation with critical power nonlinearity, Proc. Amer. Math. Soc. 111 (1991), 487-496 MR1045145 (91f:35026)
    • (1991) Proc. Amer. Math. Soc. , vol.111 , pp. 487-496
    • Ogawa, T.1    Tsutsumi, Y.2
  • 18
    • 0000540347 scopus 로고
    • Existence of solitary waves in higher dimensions
    • MR0454365 56:12616
    • W. A. Strauss, Existence of solitary waves in higher dimensions, Comm. Math. Phys. 55 (1977), 149-162. MR0454365 (56:12616)
    • (1977) Comm. Math. Phys. , vol.55 , pp. 149-162
    • Strauss, W.A.1
  • 19
    • 0040580243 scopus 로고
    • Rate of concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power
    • MR1074950 91j:35043
    • Y. Tsutsumi, Rate of concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power, Nonlinear Anal. T. M. A. 15 (1990), 719-724. MR1074950 (91j:35043)
    • (1990) Nonlinear Anal. T. M. A. , vol.15 , pp. 719-724
    • Tsutsumi, Y.1
  • 20
    • 0041473959 scopus 로고
    • Nonlinear Schrödinger equations and sharp interpolation estimates
    • MR691044 84d:35140
    • M. I. Weinstein, Nonlinear Schrödinger equations and sharp interpolation estimates, Comm. Math. Phys. 87 (1983), 567-576. MR691044 (84d:35140)
    • (1983) Comm. Math. Phys. , vol.87 , pp. 567-576
    • Weinstein, M.I.1
  • 21
    • 0036027450 scopus 로고    scopus 로고
    • Sharp conditions of global existence for nonlinear Schrödinger and Klein-Gordon equations
    • MR1870752 2002h:35303
    • J. Zhang, Sharp conditions of global existence for nonlinear Schrödinger and Klein-Gordon equations, Nonlinear Anal. T. M. A. 48 (2002), 191-207. MR1870752 (2002h:35303)
    • (2002) Nonlinear Anal. T. M. A. , vol.48 , pp. 191-207
    • Zhang, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.