메뉴 건너뛰기




Volumn 121, Issue 3, 1999, Pages 629-669

Small data blow-up for semilinear Klein-Gordon equations

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0033148075     PISSN: 00029327     EISSN: None     Source Type: Journal    
DOI: 10.1353/ajm.1999.0021     Document Type: Article
Times cited : (45)

References (45)
  • 1
  • 3
    • 0000643677 scopus 로고
    • On space-time means and everywhere defined scattering operators
    • P. Brenner, On space-time means and everywhere defined scattering operators, Math. Z. 186 (1984), 383-391.
    • (1984) Math. Z. , vol.186 , pp. 383-391
    • Brenner, P.1
  • 4
    • 84966231823 scopus 로고
    • On the asymptotic behavior of solutions of the wave equations
    • A. R. Brodsky, On the asymptotic behavior of solutions of the wave equations, Proc. Amer. Math. Soc. 18 (1967), 207-208.
    • (1967) Proc. Amer. Math. Soc. , vol.18 , pp. 207-208
    • Brodsky, A.R.1
  • 5
    • 0002601940 scopus 로고
    • Uniform estimates for solutions of nonlinear Klein-Gordon equations
    • T. Cazenave, Uniform estimates for solutions of nonlinear Klein-Gordon equations, J. Funct. Anal. 60 (1985), 36-55.
    • (1985) J. Funct. Anal. , vol.60 , pp. 36-55
    • Cazenave, T.1
  • 6
    • 23244446904 scopus 로고
    • Critical nonlinear Schrödinger equation
    • T. Cazenave and F. B. Weissler, Critical nonlinear Schrödinger equation, Nonlinear Anal. 14 (1990), 807-836.
    • (1990) Nonlinear Anal. , vol.14 , pp. 807-836
    • Cazenave, T.1    Weissler, F.B.2
  • 7
    • 0002645561 scopus 로고
    • Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation
    • M. Christ and M. Weinstein, Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation, J. Funct. Anal. 100 (1991), 87-109.
    • (1991) J. Funct. Anal. , vol.100 , pp. 87-109
    • Christ, M.1    Weinstein, M.2
  • 9
    • 0001726448 scopus 로고    scopus 로고
    • Weighted Strichartz estimates and global existence for semilinear wave equations
    • V. Georgiev, H. Lindblad, and C. D. Sogge, Weighted Strichartz estimates and global existence for semilinear wave equations, Amer. J. Math. 119 (1997), 1291-1319.
    • (1997) Amer. J. Math. , vol.119 , pp. 1291-1319
    • Georgiev, V.1    Lindblad, H.2    Sogge, C.D.3
  • 10
    • 0001547541 scopus 로고
    • On the asymptotic behavior of nonlinear wave equations
    • R. Glassey, On the asymptotic behavior of nonlinear wave equations, Trans. Amer. Math. Soc. 182 (1973). 187-200.
    • (1973) Trans. Amer. Math. Soc. , vol.182 , pp. 187-200
    • Glassey, R.1
  • 11
    • 0000337016 scopus 로고
    • Existence in the large for □u = F(u) in two dimensions
    • _, Existence in the large for □u = F(u) in two dimensions, Math. Z. 178 (1981), 233-261.
    • (1981) Math. Z. , vol.178 , pp. 233-261
  • 12
    • 0000775450 scopus 로고
    • Finite-time blowup for solutions of nonlinear wave equations
    • _, Finite-time blowup for solutions of nonlinear wave equations, Math. Z. 177 (1981), 323-340.
    • (1981) Math. Z. , vol.177 , pp. 323-340
  • 13
    • 84990574949 scopus 로고
    • Regularity for the wave equation with a critical nonlinearity
    • M. Grillakis, Regularity for the wave equation with a critical nonlinearity, Comm. Pure Appl. Math. 45 (1992), 749-774.
    • (1992) Comm. Pure Appl. Math. , vol.45 , pp. 749-774
    • Grillakis, M.1
  • 16
    • 0000774996 scopus 로고
    • Blow-up of solutions of nonlinear wave equations in three dimensions
    • F. John, Blow-up of solutions of nonlinear wave equations in three dimensions, Manuscripta Math. 28 (1979), 235-268.
    • (1979) Manuscripta Math. , vol.28 , pp. 235-268
    • John, F.1
  • 17
    • 0000119567 scopus 로고
    • Global and unique weak solutions of nonlinear wave equations
    • L. Kapitanski, Global and unique weak solutions of nonlinear wave equations. Math. Res. Lett. 1 (1994), 211-223.
    • (1994) Math. Res. Lett. , vol.1 , pp. 211-223
    • Kapitanski, L.1
  • 18
    • 84980153133 scopus 로고
    • Blow-up of solutions of some nonlinear hyperbolic equations
    • T. Kato, Blow-up of solutions of some nonlinear hyperbolic equations, Comm. Pure Appl. Math. 33 (1980), 501-505.
    • (1980) Comm. Pure Appl. Math. , vol.33 , pp. 501-505
    • Kato, T.1
  • 19
    • 84990617895 scopus 로고
    • Commutator estimates and the Euler and Navier-Stokes equations
    • T. Kato and G. Ponce, Commutator estimates and the Euler and Navier-Stokes equations, Comm. Pure Appl. Math. 41 (1988), 891-907.
    • (1988) Comm. Pure Appl. Math. , vol.41 , pp. 891-907
    • Kato, T.1    Ponce, G.2
  • 20
    • 84980081022 scopus 로고
    • On solutions of nonlinear wave equations
    • J. Keller, On solutions of nonlinear wave equations, Comm. Pure Appl. Math. 10 (1957), 523-530.
    • (1957) Comm. Pure Appl. Math. , vol.10 , pp. 523-530
    • Keller, J.1
  • 21
    • 84990619688 scopus 로고
    • Global existence of small amplitude solutions to nonlinear Klein-Gordon equations in four space-time dimensions
    • S. Klainerman, Global existence of small amplitude solutions to nonlinear Klein-Gordon equations in four space-time dimensions, Comm. Pure Appl. Math. 38 (1985), 631-641.
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 631-641
    • Klainerman, S.1
  • 22
    • 0001478425 scopus 로고
    • On existence and scattering with minimal regularity for semilinear wave equations
    • H. Lindblad and C. D. Sogge, On existence and scattering with minimal regularity for semilinear wave equations, J. Funct. Anal. 130 (1995), 357-426.
    • (1995) J. Funct. Anal. , vol.130 , pp. 357-426
    • Lindblad, H.1    Sogge, C.D.2
  • 23
    • 0009236434 scopus 로고    scopus 로고
    • Restriction theorems and semilinear Klein-Gordon equations in (1+3) dimensions
    • _, Restriction theorems and semilinear Klein-Gordon equations in (1+3) dimensions, Duke Math. J. 85 (1996), 227-252.
    • (1996) Duke Math. J. , vol.85 , pp. 227-252
  • 25
    • 0009232281 scopus 로고    scopus 로고
    • Almost global existence of solutions for the quadratic semilinear Klein-Gordon equation in one space dimension
    • K. Moriyama, S. Tonegawa, and Y. Tsutsumi, Almost global existence of solutions for the quadratic semilinear Klein-Gordon equation in one space dimension, Funkcial. Ekvac. 40 (1997), 313-333.
    • (1997) Funkcial. Ekvac. , vol.40 , pp. 313-333
    • Moriyama, K.1    Tonegawa, S.2    Tsutsumi, Y.3
  • 26
    • 0001739203 scopus 로고    scopus 로고
    • Global existence and asymptotic behavior of solutions for the Klein-Gordon equations with quadratic nonlinearity in two space dimensions
    • T. Ozawa, K. Tsutaya, and Y. Tsutsumi, Global existence and asymptotic behavior of solutions for the Klein-Gordon equations with quadratic nonlinearity in two space dimensions, Math Z. 222 (1996), 341-362.
    • (1996) Math Z. , vol.222 , pp. 341-362
    • Ozawa, T.1    Tsutaya, K.2    Tsutsumi, Y.3
  • 27
    • 0000149088 scopus 로고
    • Low energy scattering for nonlinear Klein-Gordon equations
    • H. Pecher, Low energy scattering for nonlinear Klein-Gordon equations, J. Funct. Anal. 63 (1985), 101-122.
    • (1985) J. Funct. Anal. , vol.63 , pp. 101-122
    • Pecher, H.1
  • 28
    • 0001002549 scopus 로고
    • The global Cauchy problem for a relativistic scalar field with power interactions
    • I. E. Segal, The global Cauchy problem for a relativistic scalar field with power interactions, Bull. Soc. Math. France 91 (1963), 129-135.
    • (1963) Bull. Soc. Math. France , vol.91 , pp. 129-135
    • Segal, I.E.1
  • 29
    • 84990623722 scopus 로고
    • Normal forms and quadratic nonlinear Klein-Gordon equations
    • J. Shatah, Normal forms and quadratic nonlinear Klein-Gordon equations, Comm. Pure. Appl. Math. 38 (1985), 685-696.
    • (1985) Comm. Pure. Appl. Math. , vol.38 , pp. 685-696
    • Shatah, J.1
  • 30
    • 84962991958 scopus 로고
    • Well posedness in the energy space for semilinear wave equations with critical growth
    • J. Shatah and M. Struwe, Well posedness in the energy space for semilinear wave equations with critical growth, Internat. Math. Res. Notices 7 (1994).
    • (1994) Internat. Math. Res. Notices , vol.7
    • Shatah, J.1    Struwe, M.2
  • 31
    • 0009156962 scopus 로고
    • Ph.D. thesis, Indiana Univ.
    • T. Sideris, Ph.D. thesis, Indiana Univ., 1981.
    • (1981)
    • Sideris, T.1
  • 32
    • 0000546412 scopus 로고
    • Nonexistence of global solutions to semilinear wave equations in high dimensions
    • _, Nonexistence of global solutions to semilinear wave equations in high dimensions, J. Differential Equations 52 (1984), 378-406.
    • (1984) J. Differential Equations , vol.52 , pp. 378-406
  • 33
    • 21144471784 scopus 로고
    • The Cauchy problem for nonlinear Klein-Gordon equation and applications
    • J. Simon and E. Taflin, The Cauchy problem for nonlinear Klein-Gordon equation and applications, Comm. Math. Phys. 152 (1993), 433-478.
    • (1993) Comm. Math. Phys. , vol.152 , pp. 433-478
    • Simon, J.1    Taflin, E.2
  • 36
    • 0004136765 scopus 로고
    • Princeton University Press
    • _, Harmonic Analysis, Princeton University Press, 1993.
    • (1993) Harmonic Analysis
  • 37
    • 0009234413 scopus 로고
    • On weak solutions of semi-linear hyperbolic equations
    • W. Strauss, On weak solutions of semi-linear hyperbolic equations. An. Acad. Brasil. Ciênc. 42 (1970), 645-651.
    • (1970) An. Acad. Brasil. Ciênc. , vol.42 , pp. 645-651
    • Strauss, W.1
  • 38
    • 0006806721 scopus 로고
    • Nonlinear invariant wave equations
    • Springer-Verlag, New York
    • _, Nonlinear invariant wave equations, Lecture Notes in Phys., vol. 78, Springer-Verlag, New York, 1978, pp. 197-249.
    • (1978) Lecture Notes in Phys. , vol.78 , pp. 197-249
  • 39
    • 0001684804 scopus 로고
    • Nonlinear scattering theory at low energy
    • _, Nonlinear scattering theory at low energy, J. Funct. Anal. 41 (1981), 110-133.
    • (1981) J. Funct. Anal. , vol.41 , pp. 110-133
  • 41
    • 84972553620 scopus 로고
    • Restriction of Fourier transform to quadratic surfaces and decay of solutions of wave equations
    • R. S. Strichartz, Restriction of Fourier transform to quadratic surfaces and decay of solutions of wave equations, Duke Math. J. 44 (1977), 705-774.
    • (1977) Duke Math. J. , vol.44 , pp. 705-774
    • Strichartz, R.S.1
  • 42
    • 0009153301 scopus 로고
    • Asymptotic behavior of waves
    • _, Asymptotic behavior of waves, J. Funct. Anal. 40 (1981), 341-357.
    • (1981) J. Funct. Anal. , vol.40 , pp. 341-357


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.