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Volumn 37, Issue 3, 2001, Pages 255-293

The Cauchy Problem for Nonlinear Klein-Gordon Equations in the Sobolev Spaces

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EID: 85013020039     PISSN: 00345318     EISSN: None     Source Type: Journal    
DOI: 10.2977/prims/1145477225     Document Type: Article
Times cited : (51)

References (30)
  • 2
    • 0002350320 scopus 로고
    • On space-time means and strong global solutions of nonlinear hyperbolic equations
    • Brenner, P., On space-time means and strong global solutions of nonlinear hyperbolic equations, Math. Z., 201 (1989), 45–55.
    • (1989) Math. Z. , vol.201 , pp. 45-55
    • Brenner, P.1
  • 3
    • 33750331623 scopus 로고
    • Lp-estimates of difference schemes for strictly hyperbolic systems with nons-mooth data
    • Brenner, P., Lp-estimates of difference schemes for strictly hyperbolic systems with nons-mooth data, SIAM J. Numer. Anal., 14 (1977), 1126–1144.
    • (1977) SIAM J. Numer. Anal. , vol.14 , pp. 1126-1144
    • Brenner, P.1
  • 4
    • 23244446904 scopus 로고
    • The Cauchy problem for the critical nonlinear Schrödinger equation in Hs
    • Cazenave, T. and Weissler, F. B., The Cauchy problem for the critical nonlinear Schrödinger equation in Hs, Nonlinear Anal., 14 (1990), 807–836.
    • (1990) Nonlinear Anal. , vol.14 , pp. 807-836
    • Cazenave, T.1    Weissler, F.B.2
  • 5
    • 58149363006 scopus 로고
    • Generalized Strichartz inequalities for the wave equation
    • Ginibre, J. and Velo, G., Generalized Strichartz inequalities for the wave equation, J. Funct. Anal., 133 (1995), 50–68.
    • (1995) J. Funct. Anal. , vol.133 , pp. 50-68
    • Ginibre, J.1    Velo, G.2
  • 6
    • 85050669204 scopus 로고
    • The global Cauchy problem for the nonlinear Schrödinger equation revisited
    • Ginibre, J. and Velo, G., The global Cauchy problem for the nonlinear Schrödinger equation revisited, Ann. Inst. H. Poincaré Anal. Non Linéaire, 2 (1985), 309–327.
    • (1985) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.2 , pp. 309-327
    • Ginibre, J.1    Velo, G.2
  • 7
    • 0000890194 scopus 로고
    • The global Cauchy problem for the nonlinear Klein-Gordon equation
    • Ginibre, J. and Velo, G., The global Cauchy problem for the nonlinear Klein-Gordon equation, Math. Z., 189 (1985), 487–505.
    • (1985) Math. Z. , vol.189 , pp. 487-505
    • Ginibre, J.1    Velo, G.2
  • 9
    • 84974005009 scopus 로고
    • A sharp counterexample to the local existence of low-regularity solutions to nonlinear wave equations
    • Lindblad, H., A sharp counterexample to the local existence of low-regularity solutions to nonlinear wave equations, Duke Math. J., 72 (1993), 503–539.
    • (1993) Duke Math. J. , vol.72 , pp. 503-539
    • Lindblad, H.1
  • 10
    • 0001478425 scopus 로고
    • On existence and scattering with minimal regularity for semilinear wave equations
    • Lindblad, H. and Sogge, C. D., 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
  • 12
    • 84911327549 scopus 로고
    • Existence of global strong solution for nonlinear Klein-Gordon equation
    • Motai, T., Existence of global strong solution for nonlinear Klein-Gordon equation, Funkcial. Ekvac., 32 (1989), 125–144.
    • (1989) Funkcial. Ekvac. , vol.32 , pp. 125-144
    • Motai, T.1
  • 14
    • 0001119867 scopus 로고    scopus 로고
    • Small solutions to nonlinear Schrödinger equations in the Sobolev spaces
    • Nakamura, M. and Ozawa, T., Small solutions to nonlinear Schrödinger equations in the Sobolev spaces, J. D'Anal. Math., 81 (2000), 305–329.
    • (2000) J. D'Anal. Math. , vol.81 , pp. 305-329
    • Nakamura, M.1    Ozawa, T.2
  • 15
    • 0033468098 scopus 로고    scopus 로고
    • Global solutions in the critical Sobolev space for the wave equations with nonlinearity of exponential growth
    • Nakamura, M. and Ozawa, T., Global solutions in the critical Sobolev space for the wave equations with nonlinearity of exponential growth, Math. Z., 231 (1999), 479–487.
    • (1999) Math. Z. , vol.231 , pp. 479-487
    • Nakamura, M.1    Ozawa, T.2
  • 16
    • 0000508831 scopus 로고    scopus 로고
    • The Cauchy problem for nonlinear wave equations in the homogeneous Sobolev space
    • Nakamura, M. and Ozawa, T., The Cauchy problem for nonlinear wave equations in the homogeneous Sobolev space, Ann. Inst. H. Poincaré, Phys. Théor., 71 (1999), 199–215.
    • (1999) Ann. Inst. H. Poincaré, Phys. Théor. , vol.71 , pp. 199-215
    • Nakamura, M.1    Ozawa, T.2
  • 17
    • 0041181291 scopus 로고    scopus 로고
    • Nonlinear Schrödinger equations in the Sobolev space of critical order
    • Nakamura, M. and Ozawa, T., Nonlinear Schrödinger equations in the Sobolev space of critical order, J. Funct. Anal., 150 (1998), 364–380.
    • (1998) J. Funct. Anal. , vol.150 , pp. 364-380
    • Nakamura, M.1    Ozawa, T.2
  • 18
    • 0031285644 scopus 로고    scopus 로고
    • Low energy scattering for nonlinear Schrödinger equations in fractional order Sobolev spaces
    • Nakamura, M. and Ozawa, T., Low energy scattering for nonlinear Schrödinger equations in fractional order Sobolev spaces, Rev. Math. Phys., 9 (1997), 397–410.
    • (1997) Rev. Math. Phys. , vol.9 , pp. 397-410
    • Nakamura, M.1    Ozawa, T.2
  • 19
    • 0001962910 scopus 로고    scopus 로고
    • Scattering theory for the nonlinear Klein-Gordon equation with Sobolev critical power
    • Nakanishi, K., Scattering theory for the nonlinear Klein-Gordon equation with Sobolev critical power, Internat. Math. Res. Notices, No.1 (1999), 31–60.
    • (1999) Internat. Math. Res. Notices , Issue.1 , pp. 31-60
    • Nakanishi, K.1
  • 20
    • 0000149088 scopus 로고
    • Low energy scattering for nonlinear Klein-Gordon equations
    • Pecher, H., 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
  • 21
    • 0001284137 scopus 로고
    • Nonlinear small data scattering for the wave and Klein-Gordon equation
    • Pecher, H., Nonlinear small data scattering for the wave and Klein-Gordon equation, Math. Z., 185 (1984), 261–270.
    • (1984) Math. Z. , vol.185 , pp. 261-270
    • Pecher, H.1
  • 22
    • 0039883669 scopus 로고
    • The u5 Klein-Gordon equation, II. Anomalous singularities for semilinear wave equations, Nonlinear partial differential equations and their applications
    • (Paris, 1978/1979) Res. Notes Math., 53, Pitman, Boston, Mass.-London
    • Rauch, J.I. The u5 Klein-Gordon equation, II. Anomalous singularities for semilinear wave equations, Nonlinear partial differential equations and their applications, Collége de France Seminar, Vol. I (Paris, 1978/1979), pp. 335–364, Res. Notes Math., 53, Pitman, Boston, Mass.-London, (1981).
    • (1981) Collége de France Seminar , vol.I , pp. 335-364
    • Rauch, J.I.1
  • 23
    • 0001684804 scopus 로고
    • Nonlinear scattering theory at low energy
    • Strauss, W., Nonlinear scattering theory at low energy, J. Funct. Anal., 41 (1981), 110–133.
    • (1981) J. Funct. Anal. , vol.41 , pp. 110-133
    • Strauss, W.1
  • 24
    • 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), 705–714.
    • (1977) Duke Math. J. , vol.44 , pp. 705-714
    • Strichartz, R.S.1
  • 25
    • 0001030020 scopus 로고
    • A note on Trudinger's extension of Sobolev's inequalities
    • Strichartz, R. S., A note on Trudinger's extension of Sobolev's inequalities, Indiana Univ. Math. J., 21 (1972), 841–842.
    • (1972) Indiana Univ. Math. J. , vol.21 , pp. 841-842
    • Strichartz, R.S.1
  • 28
    • 84972566488 scopus 로고
    • Scattering of solutions of nonlinear Klein-Gordon equations in three space dimensions
    • Tsutsumi, M., Scattering of solutions of nonlinear Klein-Gordon equations in three space dimensions, J. Math. Soc. Japan, 35 (1983), 521–538.
    • (1983) J. Math. Soc. Japan , vol.35 , pp. 521-538
    • Tsutsumi, M.1
  • 29
    • 0347752526 scopus 로고    scopus 로고
    • Scattering of solutions for critical and subcritical nonlinear Klein-Gordon equations in Hs
    • Wang, B., Scattering of solutions for critical and subcritical nonlinear Klein-Gordon equations in Hs, Discrete Contin. Dynam. Systems, 5 (1999), 753–763.
    • (1999) Discrete Contin. Dynam. Systems , vol.5 , pp. 753-763
    • Wang, B.1
  • 30
    • 0032012935 scopus 로고    scopus 로고
    • On existence and scattering for critical and subcritical nonlinear Klein-Gordon equations in Hs
    • Wang, B., On existence and scattering for critical and subcritical nonlinear Klein-Gordon equations in Hs, Nonlinear Anal., 31 (1998), 573–587.
    • (1998) Nonlinear Anal. , vol.31 , pp. 573-587
    • Wang, B.1


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