메뉴 건너뛰기




Volumn 134, Issue 3, 1998, Pages 489-545

Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0039165707     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002220050272     Document Type: Article
Times cited : (157)

References (52)
  • 1
    • 0001231291 scopus 로고
    • Nonlinear evolution equations in two and three dimensions
    • [AbHa] M.J. Ablowitz, R. Haberman: Nonlinear evolution equations in two and three dimensions Phys. Rev. Lett. 35, 1185-1188 (1975)
    • (1975) Phys. Rev. Lett. , vol.35 , pp. 1185-1188
    • Ablowitz, M.J.1    Haberman, R.2
  • 3
    • 77956924089 scopus 로고
    • Radial Fourier multipliers and associated maximal functions
    • [Cr] A. Carbery: Radial Fourier multipliers and associated maximal functions North Holland Math. Studies III, 49-55 (1985)
    • (1985) North Holland Math. Studies , vol.3 , pp. 49-55
    • Carbery, A.1
  • 4
    • 0003197180 scopus 로고    scopus 로고
    • An introduction to nonlinear Schrödinger equations
    • Universidade Federal do Rio de Janeiro
    • [Cz] T. Cazenave: An introduction to nonlinear Schrödinger equations Textos de Métodos Matemáticos 22 Universidade Federal do Rio de Janeiro.
    • Textos de Métodos Matemáticos , vol.22
    • Cazenave, T.1
  • 5
    • 0002738813 scopus 로고
    • Local existence for semilinear Schrödinger equations
    • H. Chihara: Local existence for semilinear Schrödinger equations Math. Japonica 42, 35-52 (1995)
    • (1995) Math. Japonica , vol.42 , pp. 35-52
    • Chihara, H.1
  • 6
    • 21444456730 scopus 로고    scopus 로고
    • The initial value problem emilinear schrödinger equations
    • H. Chihara: The initial value problem emilinear Schrödinger equations Publ. RIMS. Kyoto Univ. 32, 445-47 (1996)
    • (1996) Publ. RIMS. Kyoto Univ. , vol.32 , pp. 445-447
    • Chihara, H.1
  • 8
    • 84968508844 scopus 로고
    • Local smoothing properties of dispersive equations
    • [CoSa] P. Constantin, J.C. Saut: Local smoothing properties of dispersive equations J. Amer. Math. Soc. 1, 413-446 (1989)
    • (1989) J. Amer. Math. Soc. , vol.1 , pp. 413-446
    • Constantin, P.1    Saut, J.C.2
  • 9
    • 84990700842 scopus 로고
    • Microlocal dispersive smoothing for the Schrödinger equation
    • [CrKaSt] W. Craig, T. Kappeler, W. Strauss: Microlocal dispersive smoothing for the Schrödinger equation Comm. Pure Appl. Math. 48, 769-860 (1995)
    • (1995) Comm. Pure Appl. Math. , vol.48 , pp. 769-860
    • Craig, W.1    Kappeler, T.2    Strauss, W.3
  • 10
    • 0000541374 scopus 로고
    • On three dimensional packets of surface waves
    • [Dase] A. Davey, K. Stewartson: On three dimensional packets of surface waves Proc. R. Soc. A 338, 101-110 (1974)
    • (1974) Proc. R. Soc. A , vol.338 , pp. 101-110
    • Davey, A.1    Stewartson, K.2
  • 11
    • 0017471194 scopus 로고
    • On two-dimensional packets of capillary-gravity waves
    • [DjRe] V.D. Djordjevic, L.G. Redekopp: On two-dimensional packets of capillary-gravity waves J. Fluid Mech. 79, 703-714 (1977)
    • (1977) J. Fluid Mech. , vol.79 , pp. 703-714
    • Djordjevic, V.D.1    Redekopp, L.G.2
  • 12
    • 0000278560 scopus 로고
    • On the Cauchy problem for Schrödinger type equations and the regularity of the solutions
    • S. Doi: On the Cauchy problem for Schrödinger type equations and the regularity of the solutions J. Math. Kyoto Univ. 34, 319-328 (1994)
    • (1994) J. Math. Kyoto Univ. , vol.34 , pp. 319-328
    • Doi, S.1
  • 13
    • 0002604507 scopus 로고    scopus 로고
    • Remarks on the Cauchy problem for Schrödinger type equations
    • S. Doi: Remarks on the Cauchy problem for Schrödinger type equations Comm. P.D.E. 21, 163-178 (1996)
    • (1996) Comm. P.D.E. , vol.21 , pp. 163-178
    • Doi, S.1
  • 14
    • 0348090464 scopus 로고
    • On the initial value problem for the Davey-Stewartson systems
    • J.M. Ghidaglia, J-C. Saut: On the initial value problem for the Davey-Stewartson systems Nonlinearity 3, 475-506 (1990)
    • (1990) Nonlinearity , vol.3 , pp. 475-506
    • Ghidaglia, J.M.1    Saut, J.-C.2
  • 16
    • 0001133675 scopus 로고
    • A necessary condition for the H∞-well posed Cauchy problem for Schrödinger type equations with variable coefficients
    • [Hr] S. Hara: A necessary condition for the H∞-well posed Cauchy problem for Schrödinger type equations with variable coefficients J. Math. Kyoto Univ. 3, 287-305 (1992)
    • (1992) J. Math. Kyoto Univ. , vol.3 , pp. 287-305
    • Hara, S.1
  • 17
    • 84973997911 scopus 로고
    • Global existence of small analytic solutions to nonlinear Schrödinger equations
    • N. Hayashi: Global existence of small analytic solutions to nonlinear Schrödinger equations Duke Math. J 62, 575-59 (1991).
    • (1991) Duke Math. J , vol.62 , pp. 575-659
    • Hayashi, N.1
  • 19
    • 84972525950 scopus 로고
    • Remarks on nonlinear Schrödinger equations in one space dimension
    • [HyOz] N. Hayashi, T. Ozawa: Remarks on nonlinear Schrödinger equations in one space dimension Diff. Integral Eqs 2, 453-461 (1994)
    • (1994) Diff. Integral Eqs , vol.2 , pp. 453-461
    • Hayashi, N.1    Ozawa, T.2
  • 20
    • 84972513603 scopus 로고
    • Global existence of small solutions to the Davey-Stewartson and the Ishimori systems
    • [HySa] N. Hayashi, J-C. Saut: Global existence of small solutions to the Davey-Stewartson and the Ishimori systems Diff. Integral Eqs 8, 1657-1675 (1995)
    • (1995) Diff. Integral Eqs , vol.8 , pp. 1657-1675
    • Hayashi, N.1    Saut, J.-C.2
  • 21
    • 0010297890 scopus 로고
    • A note on the Cauchy problem for Schrödinger type equations on the Riemannian manifold
    • [Ic] W. Ichinose: A note on the Cauchy problem for Schrödinger type equations on the Riemannian manifold Math. Japonica 35, 205-213 (1990)
    • (1990) Math. Japonica , vol.35 , pp. 205-213
    • Ichinose, W.1
  • 22
    • 0002119151 scopus 로고
    • Multi vortex solutions of a two dimensional nonlinear waveequation
    • [Is] Y. Ishimori: Multi vortex solutions of a two dimensional nonlinear waveequation Progr. Theor. Phys 72, 33-37 (1984)
    • (1984) Progr. Theor. Phys , vol.72 , pp. 33-37
    • Ishimori, Y.1
  • 25
    • 0003123140 scopus 로고
    • Quasilinear evolution equation, with applications to partial differential equations
    • Springer-Verlag
    • T. Kato: Quasilinear evolution equation, with applications to partial differential equations Lecture Notes in Math. 448, 27-50, Springer-Verlag 1975.
    • (1975) Lecture Notes in Math. , vol.448 , pp. 27-50
    • Kato, T.1
  • 26
  • 27
    • 0001969794 scopus 로고
    • Oscillatory integrals and regularity of dispersive equations
    • C.E Kenig, G. Ponce, E. Vega: Oscillatory integrals and regularity of dispersive equations Indiana University Math. J. 40, 33-69 (1991)
    • (1991) Indiana University Math. J. , vol.40 , pp. 33-69
    • Kenig, C.E.1    Ponce, G.2    Vega, E.3
  • 28
    • 84894536209 scopus 로고
    • Small solutions to nonlinear Schrödinger equations
    • C.E. Kenig, G. Ponce, E. Vega: Small solutions to nonlinear Schrödinger equations Annales de l'I.H.P. 10, 255-288 (1993)
    • (1993) Annales de L'I.H.P. , vol.10 , pp. 255-288
    • Kenig, C.E.1    Ponce, G.2    Vega, E.3
  • 29
    • 84990553608 scopus 로고
    • Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle
    • C.E. Kenig, G. Ponce, L. Vega: Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle Comm. Pure Appl. Math. 46, 527-620 (1993)
    • (1993) Comm. Pure Appl. Math. , vol.46 , pp. 527-620
    • Kenig, C.E.1    Ponce, G.2    Vega, L.3
  • 30
    • 0000515612 scopus 로고
    • On the Zakharov and Zakharov-Schulman systems
    • C.E. Kenig, G. Ponce, L. Vega: On the Zakharov and Zakharov-Schulman systems J. Funct. Anal. 127, 204-234 (1995)
    • (1995) J. Funct. Anal. , vol.127 , pp. 204-234
    • Kenig, C.E.1    Ponce, G.2    Vega, L.3
  • 32
    • 0002471924 scopus 로고    scopus 로고
    • On the Cauchy problem for linear schrödinger systems with variable coefficient lower order terms
    • C.E. Kenig, G. Ponce, L. Vega: On the Cauchy problem for linear Schrödinger systems with variable coefficient lower order terms Canadian Math. Soc. Conf. Proc. 21, 205-227 (1997)
    • (1997) Canadian Math. Soc. Conf. Proc. , vol.21 , pp. 205-227
    • Kenig, C.E.1    Ponce, G.2    Vega, L.3
  • 33
    • 84968504995 scopus 로고
    • A strong type (2,2) estimate for the maximal function associated to the Schrödinger equation
    • [KeRu] C.E. Kenig, A. Ruiz: A strong type (2,2) estimate for the maximal function associated to the Schrödinger equation Trans. Amer. Math. Soc. 280, 239-246 (1983)
    • (1983) Trans. Amer. Math. Soc. , vol.280 , pp. 239-246
    • Kenig, C.E.1    Ruiz, A.2
  • 34
    • 0002394348 scopus 로고
    • Long time behavior of solutions to nonlinear evolutions equations
    • [Kl] S. Klainerman: Long time behavior of solutions to nonlinear evolutions equations Arch. Ration. Mech. and Analysis 78, 73-98 (1981)
    • (1981) Arch. Ration. Mech. and Analysis , vol.78 , pp. 73-98
    • Klainerman, S.1
  • 35
    • 84990619712 scopus 로고
    • Global small amplitude solutions to nonlinear evolution equations
    • [KlPo] S. Klainerman, G. Ponce: Global small amplitude solutions to nonlinear evolution equations Comm. Pure Appl. Math. 36, 133-141 (1983)
    • (1983) Comm. Pure Appl. Math. , vol.36 , pp. 133-141
    • Klainerman, S.1    Ponce, G.2
  • 36
    • 38249026722 scopus 로고
    • On the inverse scattering transform of the Ishimori equations
    • [KoMa] B.G. Konopelchenko, B.T. Matkarimov: On the inverse scattering transform of the Ishimori equations Phys. Lett. A 135, 183-189 (1989)
    • (1989) Phys. Lett. A , vol.135 , pp. 183-189
    • Konopelchenko, B.G.1    Matkarimov, B.T.2
  • 40
    • 84963014993 scopus 로고
    • On local regularity of schrödinger equations
    • [RuVe] A. Ruiz, L. Vega: On local regularity of Schrödinger equations Internat. Math. Res. Notices 69, 13-27 (1992)
    • (1992) Internat. Math. Res. Notices , vol.69 , pp. 13-27
    • Ruiz, A.1    Vega, L.2
  • 41
    • 0001152880 scopus 로고
    • Global existence of small solutions to nonlinear evolution equations
    • [Sh] J. Shatah: Global existence of small solutions to nonlinear evolution equations J. Diff. Eqs. 46, 409-423 (1982)
    • (1982) J. Diff. Eqs. , vol.46 , pp. 409-423
    • Shatah, J.1
  • 42
    • 0000489206 scopus 로고
    • Wave operators and analytic solutions for systems of nonlinear Klein-Gordon equations and of non-linear Schrödinger equations
    • [SiTa] J. Simon, E. Taflin: Wave operators and analytic solutions for systems of nonlinear Klein-Gordon equations and of non-linear Schrödinger equations Comm. Math. Phys. 99, 541-562 (1985)
    • (1985) Comm. Math. Phys. , vol.99 , pp. 541-562
    • Simon, J.1    Taflin, E.2
  • 43
    • 0001679726 scopus 로고
    • Regularity of solutions to the Schrödinger equations
    • [Sj] P. Sjölin: Regularity of solutions to the Schrödinger equations Duke Math. J. 55, 699-715 (1987)
    • (1987) Duke Math. J. , vol.55 , pp. 699-715
    • Sjölin, P.1
  • 44
  • 45
    • 0010245532 scopus 로고
    • On the cauchy problem for some non-kowalewskian equations with distinct characteristic roots
    • [TkI] J. Takeuchi: On the Cauchy problem for some non-kowalewskian equations with distinct characteristic roots J. Math. Kyoto Univ. 20, 105-124 (1980)
    • (1980) J. Math. Kyoto Univ. , vol.20 , pp. 105-124
    • Takeuchi, J.1
  • 46
    • 0041631975 scopus 로고
    • Le problème de Cauchy pour certaines équations aux derivées partielles du type de Schrödinger, VIII;symétrisations indépendendantes du temps
    • J. Takeuchi: Le problème de Cauchy pour certaines équations aux derivées partielles du type de Schrödinger, VIII;symétrisations indépendendantes du temps C. R. Acad. Sci. Paris t315, Série 1, 1055-1058 (1992)
    • (1992) C. R. Acad. Sci. Paris T315, Série , vol.1 , pp. 1055-1058
    • Takeuchi, J.1
  • 47
    • 0027635519 scopus 로고
    • On the H∞-well posed Cauchy problem for Schrödinger type equations
    • [Tr] S. Tarama: On the H∞-well posed Cauchy problem for Schrödinger type equations Mem. Fac. Eng. Kyoto Uni. 55, 143-153 (1993)
    • (1993) Mem. Fac. Eng. Kyoto Uni. , vol.55 , pp. 143-153
    • Tarama, S.1
  • 48
    • 0003434854 scopus 로고
    • Pseudodifferential operators and nonlinear PDE Birkhäuser
    • [Ty] M.E. Taylor: Pseudodifferential Operators and Nonlinear PDE Birkhäuser, Progress in Math. 100, (1991).
    • (1991) Progress in Math. , vol.100
    • Taylor, M.E.1
  • 49
    • 0000801121 scopus 로고
    • The Schrödinger equation: Pointwise convergence to the initial date
    • [Ve] L. Vega: The Schrödinger equation: pointwise convergence to the initial date Proc. Amer. Math. Soc. 102, 874-878 (1988)
    • (1988) Proc. Amer. Math. Soc. , vol.102 , pp. 874-878
    • Vega, L.1
  • 50
    • 0008979451 scopus 로고
    • On the microlocal smoothing effect of dispersive partial differential equations I ; second order linear equations
    • [Ym] M. Yamazaki: On the microlocal smoothing effect of dispersive partial differential equations I ; second order linear equations Algebraic Analysis 11, 911-926 (1988)
    • (1988) Algebraic Analysis , vol.11 , pp. 911-926
    • Yamazaki, M.1
  • 51
    • 0003005007 scopus 로고
    • Multi-scale expansions in the theory of systems integrable by the inverse scattering method
    • [ZaKu] V.E. Zakharov, E. A. Kuznetson: Multi-scale expansions in the theory of systems integrable by the inverse scattering method Physica D 18, 455-463 (1986)
    • (1986) Physica D , vol.18 , pp. 455-463
    • Zakharov, V.E.1    Kuznetson, E.A.2
  • 52
    • 0000071824 scopus 로고
    • Degenerated dispersion laws, motion invariant and kinetic equations
    • [ZaSc] V.E. Zakharov, E.I. Schulman: Degenerated dispersion laws, motion invariant and kinetic equations Physica ID, 185-250 (1980)
    • (1980) Physica , vol.1 D , pp. 185-250
    • Zakharov, V.E.1    Schulman, E.I.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.