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Well-posedness for the supercritical gKdV equation
1. | Universität Bielefeld, Fakultät für Mathematik, Postfach 100131, 33501 Bielefeld, Germany |
References:
[1] |
Jöran Bergh and Jörgen Löfström, "Interpolation Spaces. An Introduction", Springer-Verlag, Berlin, 1976, Grundlehren der Mathematischen Wissenschaften, No. 223.
doi: 10.1007/978-3-642-66451-9. |
[2] |
Michael Christ, James E. Colliander and Terence Tao, Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations, Amer. J. Math., 125 (2003), 1235-1293.
doi: 10.1353/ajm.2003.0040. |
[3] |
Luiz G. Farah, Felipe Linares and Ademir Pastor, The supercritical generalized KdV equation: global well-posedness in the energy space and below, Math. Res. Lett., 18 (2011), 357-377.
doi: 10.4310/MRL.2011.v18.n2.a13. |
[4] |
Axel Grünrock, A bilinear Airy-estimate with application to gKdV-3, Differential Integral Equations, 18 (2005), 1333-1339. |
[5] |
Martin Hadac, Sebastian Herr and Herbert Koch, Well-posedness and scattering for the KP-II equation in a critical space, Ann. Inst. H. Poincaré Anal. Non Linéaire, 26 (2009), 917-941, Erratum: ibid., 3 (2010), 971-972.
doi: 10.1016/j.anihpc.2008.04.002. |
[6] |
Carlos E. Kenig, Gustavo Ponce and Luis Vega, Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle, Comm. Pure Appl. Math., 46 (1993), 527-620.
doi: 10.1002/cpa.3160460405. |
[7] |
Carlos E. Kenig, Gustavo Ponce and Luis Vega, A bilinear estimate with applications to the KdV equation, J. Amer. Math. Soc., 9 (1996), 573-603.
doi: 10.1090/S0894-0347-96-00200-7. |
[8] |
Herbert Koch and Jeremy L. Marzuola, Small data scattering and soliton stability in $\dot H^{-\frac16}$ for the quartic KdV Equation, Anal. PDE, 5 (2012), 145-198.
doi: 10.2140/apde.2012.5.145. |
[9] |
Herbert Koch and Daniel Tataru, Dispersive estimates for principally normal pseudodifferential operators, Comm. Pure Appl. Math., 58 (2005), 217-284.
doi: 10.1002/cpa.20067. |
[10] |
Herbert Koch and Daniel Tataru, A priori bounds for the 1D cubic NLS in negative Sobolev spaces, Int. Math. Res. Not. IMRN, 2007 (2007), Art. ID rnm053, 36.
doi: 10.1093/imrn/rnm053. |
[11] |
Luc Molinet and Francis Ribaud, On the Cauchy problem for the generalized Korteweg-de Vries equation, Comm. Partial Differential Equations, 28 (2003), 2065-2091.
doi: 10.1081/PDE-120025496. |
[12] |
Terence Tao, Scattering for the quartic generalised Korteweg-de Vries equation, J. Differential Equations, 232 (2007), 623-651.
doi: 10.1016/j.jde.2006.07.019. |
[13] |
Norbert Wiener, The quadratic variation of a function and its fourier coefficients., Journ. Math. Phys., 3 (1924), 72-94. |
show all references
References:
[1] |
Jöran Bergh and Jörgen Löfström, "Interpolation Spaces. An Introduction", Springer-Verlag, Berlin, 1976, Grundlehren der Mathematischen Wissenschaften, No. 223.
doi: 10.1007/978-3-642-66451-9. |
[2] |
Michael Christ, James E. Colliander and Terence Tao, Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations, Amer. J. Math., 125 (2003), 1235-1293.
doi: 10.1353/ajm.2003.0040. |
[3] |
Luiz G. Farah, Felipe Linares and Ademir Pastor, The supercritical generalized KdV equation: global well-posedness in the energy space and below, Math. Res. Lett., 18 (2011), 357-377.
doi: 10.4310/MRL.2011.v18.n2.a13. |
[4] |
Axel Grünrock, A bilinear Airy-estimate with application to gKdV-3, Differential Integral Equations, 18 (2005), 1333-1339. |
[5] |
Martin Hadac, Sebastian Herr and Herbert Koch, Well-posedness and scattering for the KP-II equation in a critical space, Ann. Inst. H. Poincaré Anal. Non Linéaire, 26 (2009), 917-941, Erratum: ibid., 3 (2010), 971-972.
doi: 10.1016/j.anihpc.2008.04.002. |
[6] |
Carlos E. Kenig, Gustavo Ponce and Luis Vega, Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle, Comm. Pure Appl. Math., 46 (1993), 527-620.
doi: 10.1002/cpa.3160460405. |
[7] |
Carlos E. Kenig, Gustavo Ponce and Luis Vega, A bilinear estimate with applications to the KdV equation, J. Amer. Math. Soc., 9 (1996), 573-603.
doi: 10.1090/S0894-0347-96-00200-7. |
[8] |
Herbert Koch and Jeremy L. Marzuola, Small data scattering and soliton stability in $\dot H^{-\frac16}$ for the quartic KdV Equation, Anal. PDE, 5 (2012), 145-198.
doi: 10.2140/apde.2012.5.145. |
[9] |
Herbert Koch and Daniel Tataru, Dispersive estimates for principally normal pseudodifferential operators, Comm. Pure Appl. Math., 58 (2005), 217-284.
doi: 10.1002/cpa.20067. |
[10] |
Herbert Koch and Daniel Tataru, A priori bounds for the 1D cubic NLS in negative Sobolev spaces, Int. Math. Res. Not. IMRN, 2007 (2007), Art. ID rnm053, 36.
doi: 10.1093/imrn/rnm053. |
[11] |
Luc Molinet and Francis Ribaud, On the Cauchy problem for the generalized Korteweg-de Vries equation, Comm. Partial Differential Equations, 28 (2003), 2065-2091.
doi: 10.1081/PDE-120025496. |
[12] |
Terence Tao, Scattering for the quartic generalised Korteweg-de Vries equation, J. Differential Equations, 232 (2007), 623-651.
doi: 10.1016/j.jde.2006.07.019. |
[13] |
Norbert Wiener, The quadratic variation of a function and its fourier coefficients., Journ. Math. Phys., 3 (1924), 72-94. |
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