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Volumn 13, Issue 4, 2003, Pages 737-794

Low regularity solutions for the kadomtsev-petviashvilii equation

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EID: 0141541843     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00039-003-0429-4     Document Type: Article
Times cited : (17)

References (30)
  • 1
    • 0000466947 scopus 로고    scopus 로고
    • Uniform decay estimates for a class of oscillatory integrals and applications
    • [BS]
    • [BS] M. BEN-ARTZI, J.-C. SAUT, Uniform decay estimates for a class of oscillatory integrals and applications, Diff. Int. Eq. 12 (1999), 137-145.
    • (1999) Diff. Int. Eq. , vol.12 , pp. 137-145
    • Ben-Artzi, M.1    Saut, J.-C.2
  • 3
    • 0001285869 scopus 로고
    • On the Cauchy problem for the Kadomtsev-Petviashvili equation
    • [Bo]
    • [Bo] J. BOURGAIN, On the Cauchy problem for the Kadomtsev-Petviashvili equation, Geom. Funct. Anal. 3 (1993), 315-341.
    • (1993) Geom. Funct. Anal. , vol.3 , pp. 315-341
    • Bourgain, J.1
  • 4
    • 0000710166 scopus 로고    scopus 로고
    • Globalizing estimates for the periodic KPI equation
    • [C]
    • [C] J. COLLIANDER, Globalizing estimates for the periodic KPI equation, Illinois J. Math. 40:4 (1996), 692-698.
    • (1996) Illinois J. Math. , vol.40 , Issue.4 , pp. 692-698
    • Colliander, J.1
  • 5
    • 0141744714 scopus 로고    scopus 로고
    • Small solutions for the Kadomtsev-Petviashvili I equation
    • [CKS]
    • [CKS] J. COLLIANDER, C. KENIG, G. STAFFILANI, Small solutions for the Kadomtsev-Petviashvili I equation, Mosc. Math. J. 1:4 (2001), 491-520.
    • (2001) Mosc. Math. J. , vol.1 , Issue.4 , pp. 491-520
    • Colliander, J.1    Kenig, C.2    Staffilani, G.3
  • 6
    • 0009367957 scopus 로고
    • Cauchy problem for the generalized Kadomtsev-Petviashvili equation
    • [F]
    • [F] A.V. FAMINSKII, Cauchy problem for the generalized Kadomtsev-Petviashvili equation, Sibirsk. Mat. Zh. 33 (1992), 160-172.
    • (1992) Sibirsk. Mat. Zh. , vol.33 , pp. 160-172
    • Faminskii, A.V.1
  • 7
    • 0001605032 scopus 로고
    • On the solvability of the N-wave, Davey-Stewartson and Kadomtsev-Petviashvili equations
    • [FoS]
    • [FoS] A.S. FOKAS, L.Y. SUNG, On the solvability of the N-wave, Davey-Stewartson and Kadomtsev-Petviashvili equations, Inverse Problems 8 (1992), 673-708.
    • (1992) Inverse Problems , vol.8 , pp. 673-708
    • Fokas, A.S.1    Sung, L.Y.2
  • 8
    • 0031574596 scopus 로고    scopus 로고
    • On the Cauchy problem for the Zakharov system
    • [GTV]
    • [GTV] J. GINIBRE, Y. TSUTSUMI, G. VELO, On the Cauchy problem for the Zakharov system, J. Funct. Anal. 151:2 (1997), 384-436.
    • (1997) J. Funct. Anal. , vol.151 , Issue.2 , pp. 384-436
    • Ginibre, J.1    Tsutsumi, Y.2    Velo, G.3
  • 11
    • 0141856294 scopus 로고    scopus 로고
    • Regularizing effects for the linearized Kadomtsev-Petviashvili (KP) equation
    • [IsMS2]
    • [IsMS2] P.J. ISAZA, J.L. MEJÍA, V. STALLBOHM, Regularizing effects for the linearized Kadomtsev-Petviashvili (KP) equation, Rev. Colombiana Mat. 31 (1997), 37-61.
    • (1997) Rev. Colombiana Mat. , vol.31 , pp. 37-61
    • Isaza, P.J.1    Mejía, J.L.2    Stallbohm, V.3
  • 12
    • 0000262859 scopus 로고
    • On the stability of solitary waves in weakly dispersive media
    • [KP]
    • [KP] B.B. KADOMTSEV, V.I. PETVIASHVILI, On the stability of solitary waves in weakly dispersive media, Soviet Phys. Dokl. 15 (1970), 539-541.
    • (1970) Soviet Phys. Dokl. , vol.15 , pp. 539-541
    • Kadomtsev, B.B.1    Petviashvili, V.I.2
  • 13
    • 84974004169 scopus 로고
    • The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices
    • [KePV1]
    • [KePV1] C. KENIG, G. PONCE, L. VEGA, The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices, Duke Math. J. 71:1 (1993), 1-21.
    • (1993) Duke Math. J. , vol.71 , Issue.1 , pp. 1-21
    • Kenig, C.1    Ponce, G.2    Vega, L.3
  • 14
    • 0001969794 scopus 로고
    • Oscillatory integrals and regularity of dispersive equations
    • [KePV2]
    • [KePV2] C. KENIG, G. PONCE, L. VEGA, Oscillatory integrals and regularity of dispersive equations, Indiana Univ. Math. J. 40 (1991), 33-69.
    • (1991) Indiana Univ. Math. J. , vol.40 , pp. 33-69
    • Kenig, C.1    Ponce, G.2    Vega, L.3
  • 15
    • 84990553608 scopus 로고
    • Well-posedness and scattering results for generalized Korteweg-de Vries equation via the contraction principle
    • [KePVS]
    • [KePVS] C. KENIG, G. PONCE, L. VEGA, Well-posedness and scattering results for generalized Korteweg-de Vries equation via the contraction principle, Comm. Pure Appl. Math. 46 (1993), 527-620.
    • (1993) Comm. Pure Appl. Math. , vol.46 , pp. 527-620
    • Kenig, C.1    Ponce, G.2    Vega, L.3
  • 16
    • 84974004169 scopus 로고
    • The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices
    • [KePV4]
    • [KePV4] C. KENIG, G. PONCE, L. VEGA, The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices, Duke Math. J. 71:1 (1993), 1-21.
    • (1993) Duke Math. J. , vol.71 , Issue.1 , pp. 1-21
    • Kenig, C.1    Ponce, G.2    Vega, L.3
  • 18
    • 0030528276 scopus 로고    scopus 로고
    • A bilinear estimate with applications to KdV equations
    • [KePV6]
    • [KePV6] C. KENIG, G. PONCE, L. VEGA, A bilinear estimate with applications to KdV equations, J. AMS 9 (1996), 573-603.
    • (1996) J. AMS , vol.9 , pp. 573-603
    • Kenig, C.1    Ponce, G.2    Vega, L.3
  • 19
    • 0036435316 scopus 로고    scopus 로고
    • The global Cauchy problem in Bourgain's type spaces for a dispersive dissipative semilinear equation
    • [MR1]
    • [MR1] L. MOLINET, F. RIBAUD, The global Cauchy problem in Bourgain's type spaces for a dispersive dissipative semilinear equation, SIAM J. Math. Anal. 33:6 (2002), 1269-1296.
    • (2002) SIAM J. Math. Anal. , vol.33 , Issue.6 , pp. 1269-1296
    • Molinet, L.1    Ribaud, F.2
  • 20
    • 0036041152 scopus 로고    scopus 로고
    • On the low regularity of the Korteweg-de Vries-Burgers equation
    • [MR2]
    • [MR2] L. MOLINET, F. RIBAUD, On the low regularity of the Korteweg-de Vries-Burgers equation, Int. Math. Res. Not. 2002, no. 37, 1979-2005.
    • Int. Math. Res. Not. , vol.2002 , Issue.37 , pp. 1979-2005
    • Molinet, L.1    Ribaud, F.2
  • 21
    • 0036872348 scopus 로고    scopus 로고
    • Well-posedness and ill- Posedness results for the Kadomtsev-Petviashvili-I equation
    • [MST1]
    • [MST1] L. MOLINET, J.-C. SAUT, N. TZVETKOV, Well-posedness and ill- posedness results for the Kadomtsev-Petviashvili-I equation, Duke. Math. J. 115:2 (2002), 353-384.
    • (2002) Duke. Math. J. , vol.115 , Issue.2 , pp. 353-384
    • Molinet, L.1    Saut, J.-C.2    Tzvetkov, N.3
  • 22
    • 0035981378 scopus 로고    scopus 로고
    • Global well-posedness for the KP-I equation
    • [MST2]
    • [MST2] L. MOLINET, J.-C. SAUT, N. TZVETKOV, Global well-posedness for the KP-I equation, Math. Ann. 324:2 (2002), 255-275.
    • (2002) Math. Ann. , vol.324 , Issue.2 , pp. 255-275
    • Molinet, L.1    Saut, J.-C.2    Tzvetkov, N.3
  • 23
    • 0001349105 scopus 로고
    • Remarks on generalized Kadomtsev-Petviashvili equations
    • [S]
    • [S] J.-C. SAUT, Remarks on generalized Kadomtsev-Petviashvili equations, Indiana Math. J. 42:3, (1993), 1011-1026.
    • (1993) Indiana Math. J. , vol.42 , Issue.3 , pp. 1011-1026
    • Saut, J.-C.1
  • 24
    • 0033586165 scopus 로고    scopus 로고
    • The Cauchy problem for higher-order KP equations
    • [ST]
    • [ST] J.-C. SAUT, N. TZVETKOV, The Cauchy problem for higher-order KP equations, J. Differential Equations 153:1 (1999), 196-222.
    • (1999) J. Differential Equations , vol.153 , Issue.1 , pp. 196-222
    • Saut, J.-C.1    Tzvetkov, N.2
  • 25
    • 38249034207 scopus 로고
    • Periodic solutions of Kadomtsev-Petviashvili equations
    • [Sc]
    • [Sc] M. SCHWARZ, Periodic solutions of Kadomtsev-Petviashvili equations, Adv. Math. 66 (1987), 217-233.
    • (1987) Adv. Math. , vol.66 , pp. 217-233
    • Schwarz, M.1
  • 26
    • 0141856292 scopus 로고    scopus 로고
    • Time local well-posedness for the Kadomtsev-Petviashvili II equation
    • [T]
    • [T] H. TAKAOKA, Time local well-posedness for the Kadomtsev-Petviashvili II equation, Harmonic Analysis and Nonlinear PDE 1102 (1999), 1-8.
    • (1999) Harmonic Analysis and Nonlinear PDE , vol.1102 , pp. 1-8
    • Takaoka, H.1
  • 27
    • 0002346079 scopus 로고    scopus 로고
    • On the local regularity of Kadomtsev- Petviashvili II equation
    • [TT]
    • [TT] H. TAKAOKA, N. TZVETKOV, On the local regularity of Kadomtsev- Petviashvili II equation, Internat. Math. Res. Notices 2 (2001), 77-114.
    • (2001) Internat. Math. Res. Notices , vol.2 , pp. 77-114
    • Takaoka, H.1    Tzvetkov, N.2
  • 28
    • 0000595598 scopus 로고    scopus 로고
    • On the generalized Kadomtsev-Petviashvili equation
    • [To]
    • [To] M.M. TOM, On the generalized Kadomtsev-Petviashvili equation, Contemp. Math. AMS 200 (1996), 193-210.
    • (1996) Contemp. Math. AMS , vol.200 , pp. 193-210
    • Tom, M.M.1
  • 29
    • 0001300143 scopus 로고
    • Local solutions of the Kadomtsev-Petviashvili equation
    • [U]
    • [U] S. UKAI, Local solutions of the Kadomtsev-Petviashvili equation, J. Fac. Sci. Univ. Tokyo Sect. 1A Math. 36 (1989), 193-209.
    • (1989) J. Fac. Sci. Univ. Tokyo Sect. 1A Math. , vol.36 , pp. 193-209
    • Ukai, S.1
  • 30
    • 0001667050 scopus 로고
    • Inverse scattering transform for the time dependent Schrödinger equations with application to the KP-I equations
    • [Z]
    • [Z] X. ZHOU, Inverse scattering transform for the time dependent Schrödinger equations with application to the KP-I equations, Comm. Math. Phys. 128 (1990), 551-564.
    • (1990) Comm. Math. Phys. , vol.128 , pp. 551-564
    • Zhou, X.1


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