메뉴 건너뛰기




Volumn , Issue 46, 2005, Pages 2815-2828

Blowup theory for the critical nonlinear schrödinger equations revisited

Author keywords

[No Author keywords available]

Indexed keywords


EID: 28444450137     PISSN: 10737928     EISSN: 16870247     Source Type: Journal    
DOI: 10.1155/imrn.2005.2815     Document Type: Review
Times cited : (182)

References (18)
  • 1
    • 0033074557 scopus 로고    scopus 로고
    • High frequency approximation of solutions to critical nonlinear wave equations
    • H. Bahouri and P. Gérard, High frequency approximation of solutions to critical nonlinear wave equations, Amer. J. Math. 121 (1999), no. 1, 131-175.
    • (1999) Amer. J. Math. , vol.121 , Issue.1 , pp. 131-175
    • Bahouri, H.1    Gérard, P.2
  • 2
    • 28444487069 scopus 로고    scopus 로고
    • Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain
    • V. Banica, Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 3 (2004), no. 1, 139-170.
    • (2004) Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) , vol.3 , Issue.1 , pp. 139-170
    • Banica, V.1
  • 3
    • 5444256656 scopus 로고    scopus 로고
    • Semilinear Schrödinger equations
    • New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Rhode Island
    • T. Cazenave, Semilinear Schrödinger Equations, Courant Lecture Notes in Mathematics, vol. 10, New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Rhode Island, 2003.
    • (2003) Courant Lecture Notes in Mathematics , vol.10
    • Cazenave, T.1
  • 4
    • 84996132207 scopus 로고    scopus 로고
    • Description du défaut de compacité de l'injection de Sobolev
    • French
    • P. Gérard, Description du défaut de compacité de l'injection de Sobolev [Description of the lack of compactness of a Sobolev embedding], ESAIM Control Optim. Calc. Var. 3 (1998), 213-233 (French).
    • (1998) ESAIM Control Optim. Calc. Var. , vol.3 , pp. 213-233
    • Gérard, P.1
  • 5
    • 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), no. 1, 1-32.
    • (1979) J. Funct. Anal. , vol.32 , Issue.1 , pp. 1-32
    • Ginibre, J.1    Velo, G.2
  • 6
    • 36749114276 scopus 로고
    • On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations
    • R. T. Glassey, On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations, J. Math. Phys. 18 (1977), no. 9, 1794-1797.
    • (1977) J. Math. Phys. , vol.18 , Issue.9 , pp. 1794-1797
    • Glassey, R.T.1
  • 7
    • 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 (2001), no. 2, 353-392.
    • (2001) J. Differential Equations , vol.175 , Issue.2 , pp. 353-392
    • Keraani, S.1
  • 9
    • 85030707196 scopus 로고
    • The concentration-compactness principle in the calculus of variations. The locally compact case. I
    • P.-L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case. I, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984), no. 2, 109-145.
    • (1984) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.1 , Issue.2 , pp. 109-145
    • Lions, P.-L.1
  • 10
    • 0001337201 scopus 로고
    • Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity
    • F. Merle, Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity, Comm. Math. Phys. 129 (1990), no. 2, 223-240.
    • (1990) Comm. Math. Phys. , vol.129 , Issue.2 , pp. 223-240
    • Merle, F.1
  • 11
    • 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), no. 2, 427-454.
    • (1993) Duke Math. J. , vol.69 , Issue.2 , pp. 427-454
  • 12
    • 0003278684 scopus 로고    scopus 로고
    • Blow-up phenomena for critical nonlinear Schrödinger and Zakharov equations
    • Proceedings of the International Congress of Mathematicians, (Berlin, 1998)
    • _, Blow-up phenomena for critical nonlinear Schrödinger and Zakharov equations, Doc. Math. (1998), 57-66, Proceedings of the International Congress of Mathematicians, Vol. III (Berlin, 1998).
    • (1998) Doc. Math. , vol.3 , pp. 57-66
  • 13
    • 0000704928 scopus 로고
    • 2 concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity
    • 2 concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity, J. Differential Equations 84 (1990), no. 2, 205-214.
    • (1990) J. Differential Equations , vol.84 , Issue.2 , pp. 205-214
    • Merle, F.1    Tsutsumi, Y.2
  • 14
    • 0003230098 scopus 로고    scopus 로고
    • The nonlinear Schrödinger equation. Self-focusing and wave collapse
    • Springer, New York
    • C. Sulem and P.-L. Sulem, The Nonlinear Schrödinger Equation. Self-Focusing and Wave Collapse, Applied Mathematical Sciences, vol. 139, Springer, New York, 1999.
    • (1999) Applied Mathematical Sciences , vol.139
    • Sulem, C.1    Sulem, P.-L.2
  • 15
    • 0040580243 scopus 로고
    • 2 concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power
    • 2 concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power, Nonlinear Anal. 15 (1990), no. 8, 719-724.
    • (1990) Nonlinear Anal. , vol.15 , Issue.8 , pp. 719-724
    • Tsutsumi, Y.1
  • 16
    • 0041473959 scopus 로고
    • Nonlinear Schrödinger equations and sharp interpolation estimates
    • M. I. Weinstein, Nonlinear Schrödinger equations and sharp interpolation estimates, Comm. Math. Phys. 87 (1982), no. 4, 567-576.
    • (1982) Comm. Math. Phys. , vol.87 , Issue.4 , pp. 567-576
    • Weinstein, M.I.1
  • 17
    • 0001295566 scopus 로고
    • On the structure and formation of singularities in solutions to nonlinear dispersive evolution equations
    • _, On the structure and formation of singularities in solutions to nonlinear dispersive evolution equations, Comm. Partial Differential Equations 11 (1986), no. 5, 545-565.
    • (1986) Comm. Partial Differential Equations , vol.11 , Issue.5 , pp. 545-565
  • 18
    • 0009156882 scopus 로고
    • The nonlinear Schrödinger equation - Singularity formation, stability and dispersion
    • The Connection between Infinite-Dimensional and Finite-Dimensional Dynamical Systems (Boulder, Colo, 1987), American Mathematical Society, Rhode Island
    • _, The nonlinear Schrödinger equation - singularity formation, stability and dispersion, The Connection between Infinite-Dimensional and Finite-Dimensional Dynamical Systems (Boulder, Colo, 1987), Contemp. Math., vol. 99, American Mathematical Society, Rhode Island, 1989, pp. 213-232.
    • (1989) Contemp. Math. , vol.99 , pp. 213-232


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.