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Volumn 2007, Issue , 2007, Pages 1-22

Local ill-posedness of the 1D Zakharov system

Author keywords

Cauchy problem; Local ill posedness; Local well posedness; Zakharov system

Indexed keywords


EID: 33847023877     PISSN: None     EISSN: 10726691     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (37)

References (11)
  • 1
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    • On wellposedness of the Zakharov system
    • MR MR1405972 97h:35206
    • J. Bourgain and J. Colliander, On wellposedness of the Zakharov system, Internat. Math. Res. Notices (1996), no. 11, 515-546. MR MR1405972 (97h:35206)
    • (1996) Internat. Math. Res. Notices , Issue.11 , pp. 515-546
    • Bourgain, J.1    Colliander, J.2
  • 2
    • 0030158684 scopus 로고    scopus 로고
    • On the illposedness of the IVP for the generalized Korteweg-de Vries and nonlinear Schrödinger equations
    • MR1396718 97d:35233
    • Björn Birnir, Carlos E. Kenig, Gustavo Ponce, Nils Svanstedt, and Luis Vega, On the illposedness of the IVP for the generalized Korteweg-de Vries and nonlinear Schrödinger equations, J. London Math. Soc. (2) 53 (1996), no. 3, 551-559. MR1396718 (97d:35233)
    • (1996) J. London Math. Soc. (2) , vol.53 , Issue.3 , pp. 551-559
    • Birnir, B.1    Kenig, C.E.2    Ponce, G.3    Svanstedt, N.4    Vega, L.5
  • 3
    • 34250084341 scopus 로고
    • Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I. Schrödinger equations
    • MR1209299 95d:35160a
    • J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I. Schrödinger equations, Geom. Funct. Anal. 3 (1993), no. 2, 107-156. MR1209299 (95d:35160a)
    • (1993) Geom. Funct. Anal , vol.3 , Issue.2 , pp. 107-156
    • Bourgain, J.1
  • 4
    • 0348218177 scopus 로고    scopus 로고
    • Michael Christ, James Colliander, and Terence Tao, Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations, Amer. J. Math. 125 (2003), no. 6, 1235-1293. MR2018661 (2005d:35223)
    • Michael Christ, James Colliander, and Terence Tao, Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations, Amer. J. Math. 125 (2003), no. 6, 1235-1293. MR2018661 (2005d:35223)
  • 5
    • 33847078173 scopus 로고    scopus 로고
    • Michael Christ, James Colliander, and Terence Tao, Ill-posedness for nonlinear Schrödinger and wave equations, to appear, Ann. Inst. H. Poincaré Anal. Non Linéaire, arxiv.org preprint math.AP/0311048.
    • Michael Christ, James Colliander, and Terence Tao, Ill-posedness for nonlinear Schrödinger and wave equations, to appear, Ann. Inst. H. Poincaré Anal. Non Linéaire, arxiv.org preprint math.AP/0311048.
  • 7
    • 0031574596 scopus 로고    scopus 로고
    • J. Ginibre, Y. Tsutsumi, and G. Velo, On the Cauchy problem for the Zakharov system, J. Funct. Anal. 151 (1997), no. 2, 384-436. MR1491547 (2000c:35220)
    • J. Ginibre, Y. Tsutsumi, and G. Velo, On the Cauchy problem for the Zakharov system, J. Funct. Anal. 151 (1997), no. 2, 384-436. MR1491547 (2000c:35220)
  • 9
    • 0001442617 scopus 로고    scopus 로고
    • Carlos E. Kenig, Gustavo Ponce, and Luis Vega, On the ill-posedness of some canonical dispersive equations, Duke Math. J. 106 (2001), no. 3, 617-633. MR1813239 (2002c:35265)
    • Carlos E. Kenig, Gustavo Ponce, and Luis Vega, On the ill-posedness of some canonical dispersive equations, Duke Math. J. 106 (2001), no. 3, 617-633. MR1813239 (2002c:35265)
  • 11
    • 21344478748 scopus 로고
    • Orbital stability of solitary waves of Zakharov system
    • MR1271934 95e:35170
    • Ya Ping Wu, Orbital stability of solitary waves of Zakharov system, J. Math. Phys. 35 (1994), no. 5, 2413-2422. MR1271934 (95e:35170)
    • (1994) J. Math. Phys , vol.35 , Issue.5 , pp. 2413-2422
    • Ya Ping, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.