메뉴 건너뛰기




Volumn 211, Issue 1, 2004, Pages 173-218

Multilinear estimates for periodic KdV equations, and applications

Author keywords

Bilinear estimates; Korteweg de Vries equation; Multilinear harmonic analysis; Nonlinear dispersive equations

Indexed keywords


EID: 2642562683     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-1236(03)00218-0     Document Type: Article
Times cited : (185)

References (30)
  • 2
    • 0001561643 scopus 로고
    • Self-spreading and strength of singularities for solutions to semilinear wave equations
    • M. Beals, Self-spreading and strength of singularities for solutions to semilinear wave equations, Ann. Math. 118 (1983) 187-214.
    • (1983) Ann. Math. , vol.118 , pp. 187-214
    • Beals, M.1
  • 4
    • 0030158684 scopus 로고    scopus 로고
    • On the ill-posedness of the IVP for the generalized KdV and nonlinear Schrödinger equations
    • B. Birnir, C. Kenig, G. Ponce, N. Svanstedt, L. Vega, On the ill-posedness of the IVP for the generalized KdV and nonlinear Schrödinger equations, J. London Math. Soc. 53 (1996) 551-559.
    • (1996) J. London Math. Soc. , vol.53 , pp. 551-559
    • Birnir, B.1    Kenig, C.2    Ponce, G.3    Svanstedt, N.4    Vega, L.5
  • 5
    • 34250084341 scopus 로고
    • Fourier restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations, Parts I; II
    • 3(3) (1993) 209-262
    • J. Bourgain, Fourier restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations, Parts I; II, Geometric Funct. Anal. 3(2) (1993) 107-156; 3(3) (1993) 209-262.
    • (1993) Geometric Funct. Anal. , vol.3 , Issue.2 , pp. 107-156
    • Bourgain, J.1
  • 6
    • 21344446988 scopus 로고
    • On the Cauchy problem for periodic KdV-type equations
    • Proceedings of the Conference in honor of Jean-Pierre Kahane (Orsay, 1993)
    • J. Bourgain, On the Cauchy problem for periodic KdV-type equations, Proceedings of the Conference in honor of Jean-Pierre Kahane (Orsay, 1993), J. Fourier Anal. Appl. (1995) 17-86.
    • (1995) J. Fourier Anal. Appl. , pp. 17-86
    • Bourgain, J.1
  • 7
    • 0000044382 scopus 로고    scopus 로고
    • Periodic Korteweg de Vries equation with measures as initial data
    • J. Bourgain, Periodic Korteweg de Vries equation with measures as initial data, Selecta Math. (N.S.) 3 (1997) 115-159.
    • (1997) Selecta Math. (N.S.) , vol.3 , pp. 115-159
    • Bourgain, J.1
  • 10
    • 0036345464 scopus 로고    scopus 로고
    • Global well-posedness for the Schrodinger equations with derivative
    • J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Global well-posedness for the Schrodinger equations with derivative, SIAM J. Math. Anal. 33 (1) (2001) 649-699.
    • (2001) SIAM J. Math. Anal. , vol.33 , Issue.1 , pp. 649-699
    • Colliander, J.1    Keel, M.2    Staffilani, G.3    Takaoka, H.4    Tao, T.5
  • 11
    • 0036771238 scopus 로고    scopus 로고
    • Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation
    • J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation, Math. Res. Lett. 9 (5-6) (2002) 659-682.
    • (2002) Math. Res. Lett. , vol.9 , Issue.5-6 , pp. 659-682
    • Colliander, J.1    Keel, M.2    Staffilani, G.3    Takaoka, H.4    Tao, T.5
  • 12
    • 0037287349 scopus 로고    scopus 로고
    • A refined global well-posedness for the Schrodinger equations with derivative
    • J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, A refined global well-posedness for the Schrodinger equations with derivative, SIAM J. Math. Anal. 34 (1) (2002) 64-86.
    • (2002) SIAM J. Math. Anal. , vol.34 , Issue.1 , pp. 64-86
    • Colliander, J.1    Keel, M.2    Staffilani, G.3    Takaoka, H.4    Tao, T.5
  • 14
    • 85030876743 scopus 로고    scopus 로고
    • Further global well-posedness results for the 2D cubic NLS, in preparation
    • J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Further global well-posedness results for the 2D cubic NLS, in preparation.
    • Colliander, J.1    Keel, M.2    Staffilani, G.3    Takaoka, H.4    Tao, T.5
  • 17
    • 0001426659 scopus 로고
    • Uniqueness for the generalized Korteweg-de Vries equations
    • J. Ginibre, Y. Tsutsumi, Uniqueness for the generalized Korteweg-de Vries equations, SIAM J. Math. Anal. 20 (1989) 1388-1425.
    • (1989) SIAM J. Math. Anal. , vol.20 , pp. 1388-1425
    • Ginibre, J.1    Tsutsumi, Y.2
  • 18
    • 85030882435 scopus 로고    scopus 로고
    • A bilinear airy-estimate with application to gKdV-3, preprint
    • A. Gruenrock, A bilinear airy-estimate with application to gKdV-3, preprint.
    • Gruenrock, A.1
  • 19
    • 0001646511 scopus 로고    scopus 로고
    • 1+1 for rough data
    • 1+1 for rough data, IMRN 21 (1998) 1117-1156.
    • (1998) IMRN , vol.21 , pp. 1117-1156
    • Keel, M.1    Tao, T.2
  • 20
    • 85030877931 scopus 로고    scopus 로고
    • Global well-posedness of the Maxwell-Klein-Gordon equation below the energy norm, to appear
    • M. Keel, T. Tao, Global well-posedness of the Maxwell-Klein-Gordon equation below the energy norm, to appear.
    • Keel, M.1    Tao, T.2
  • 21
    • 84990553608 scopus 로고
    • Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle
    • C. 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 (1993) 527-560.
    • (1993) Comm. Pure Appl. Math. , vol.46 , pp. 527-560
    • Kenig, C.1    Ponce, G.2    Vega, L.3
  • 22
    • 84974004169 scopus 로고
    • The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices
    • 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 (1993) 1-21.
    • (1993) Duke Math. J. , vol.71 , pp. 1-21
    • Kenig, C.1    Ponce, G.2    Vega, L.3
  • 23
    • 0030528276 scopus 로고    scopus 로고
    • A bilinear estimate with applications to the KdV equation
    • C. Kenig, G. Ponce, L. Vega, A bilinear estimate with applications to the KdV equation, J. Amer. Math. Soc. 9 (1996) 573-603.
    • (1996) J. Amer. Math. Soc. , vol.9 , pp. 573-603
    • Kenig, C.1    Ponce, G.2    Vega, L.3
  • 24
    • 0001442617 scopus 로고    scopus 로고
    • On the ill-posedness of some canonical dispersive equations
    • C. Kenig, G. Ponce, L. Vega, On the ill-posedness of some canonical dispersive equations, Duke Math. J. 106 (2001) 617-633.
    • (2001) Duke Math. J. , vol.106 , pp. 617-633
    • Kenig, C.1    Ponce, G.2    Vega, L.3
  • 25
    • 84973999554 scopus 로고
    • Smoothing estimates for null forms and applications
    • S. Klainerman, M. Machedon, Smoothing estimates for null forms and applications, Duke Math J. 81 (1995) 99-103.
    • (1995) Duke Math J. , vol.81 , pp. 99-103
    • Klainerman, S.1    Machedon, M.2
  • 26
    • 0006772025 scopus 로고
    • Infinite-dimensional symplectic capacities and a squeezing theorem for Hamiltonian PDEs
    • S.B. Kuksin, Infinite-dimensional symplectic capacities and a squeezing theorem for Hamiltonian PDEs, Comm. Math. Phys. 167 (3) (1995) 531-552.
    • (1995) Comm. Math. Phys. , vol.167 , Issue.3 , pp. 531-552
    • Kuksin, S.B.1
  • 27
    • 84972568928 scopus 로고
    • Nonlinear microlocal analysis of semilinear hyperbolic systems in one space dimension
    • J. Rauch, M. Reed, Nonlinear microlocal analysis of semilinear hyperbolic systems in one space dimension, Duke Math. J. 49 (1982) 397-475.
    • (1982) Duke Math. J. , vol.49 , pp. 397-475
    • Rauch, J.1    Reed, M.2
  • 28
    • 0003913685 scopus 로고    scopus 로고
    • Multilinear space time estimates and applications to local existence theory for non-linear wave equations
    • Princeton University Thesis
    • S. Selberg, Multilinear space time estimates and applications to local existence theory for non-linear wave equations, Princeton University Thesis, 1999.
    • (1999)
    • Selberg, S.1
  • 29
    • 1842765689 scopus 로고    scopus 로고
    • On solutions for periodic generalized KdV equations
    • G. Staffilani, On solutions for periodic generalized KdV equations, IMRN 18 (1997) 899-917.
    • (1997) IMRN , vol.18 , pp. 899-917
    • Staffilani, G.1
  • 30
    • 0035486554 scopus 로고    scopus 로고
    • 2 functions, and applications to non-linear dispersive equations
    • 2 functions, and applications to non-linear dispersive equations, Amer. J. Math. 123 (5) (2001) 890-908.
    • (2001) Amer. J. Math. , vol.123 , Issue.5 , pp. 890-908
    • Tao, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.