Well-Posedness and Scattering for the KP-II Equation in a Critical Space
Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 3, p. 917-941
@article{AIHPC_2009__26_3_917_0,
     author = {Hadac, Martin and Herr, Sebastian and Koch, Herbert},
     title = {Well-Posedness and Scattering for the KP-II Equation in a Critical Space},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {26},
     number = {3},
     year = {2009},
     pages = {917-941},
     doi = {10.1016/j.anihpc.2008.04.002},
     zbl = {1169.35372},
     mrnumber = {2526409},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2009__26_3_917_0}
}
Hadac, Martin; Herr, Sebastian; Koch, Herbert. Well-Posedness and Scattering for the KP-II Equation in a Critical Space. Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 3, pp. 917-941. doi : 10.1016/j.anihpc.2008.04.002. http://www.numdam.org/item/AIHPC_2009__26_3_917_0/

[1] Biondini G., Chakravarty S., Elastic and Inelastic Line-Soliton Solutions of the Kadomtsev-Petviashvili II Equation, Math. Comput. Simulation 74 (2-3) (2007) 237-250. | MR 2307861 | Zbl 1118.35041

[2] Bourgain J., On the Cauchy Problem for the Kadomtsev-Petviashvili Equation, Geom. Funct. Anal. 3 (4) (1993) 315-341. | MR 1223434 | Zbl 0787.35086

[3] Christ M., Colliander J., Tao T., Asymptotics, Frequency Modulation, and Low Regularity Ill-Posedness for Canonical Defocusing Equations, Amer. J. Math. 125 (6) (2003) 1235-1293. | MR 2018661 | Zbl 1048.35101

[4] Dickey L. A., Soliton Equations and Hamiltonian Systems, Advanced Series in Mathematical Physics, vol. 26, second ed., World Scientific Publishing Co. Inc., River Edge, NJ, 2003. | MR 1964513 | Zbl 1140.35012

[5] Federer H., Geometric Measure Theory, Reprint of the 1969 edition, Classics in Mathematics, Springer-Verlag, Berlin, 1996. | MR 257325 | Zbl 0874.49001

[6] Ginibre J., Tsutsumi Y., Velo G., On the Cauchy Problem for the Zakharov System, J. Funct. Anal. 151 (2) (1997) 384-436. | MR 1491547 | Zbl 0894.35108

[7] M. Hadac, Well-posedness for the Kadomtsev-Petviashvili II equation and generalisations, Trans. Amer. Math. Soc., in press. | MR 2434299 | Zbl 1157.35094

[8] Isaza J. Pedro, Mejía L. Jorge, Global Solution for the Kadomtsev-Petviashvili Equation (KPII) in Anisotropic Sobolev Spaces of Negative Indices, Electron. J. Differential Equations 68 (2003), 12 pp. (electronic). | MR 1993776 | Zbl 1037.35068

[9] Kadomtsev B. B., Petviashvili V. I., On the Stability of Solitary Waves in Weakly Dispersing Media, Sov. Phys. Dokl. 15 (1970) 539-541. | Zbl 0217.25004

[10] Kenig C. E., Ziesler S. N., Local Well Posedness for Modified Kadomstev-Petviashvili Equations, Differential Integral Equations 18 (10) (2005) 1111-1146. | MR 2162626

[11] Kiselev O. M., Asymptotics of Solutions of Multidimensional Integrable Equations and Their Perturbations, J. Math. Sci., New York 138 (6) (2006) 6067-6230, Translated from Sovremennaya Matematika. Fundamental'nye Napravleniya, vol. 11, Differential Equations, 2004. | MR 2120870 | Zbl pre02204906

[12] Koch H., Tataru D., Dispersive Estimates for Principally Normal Pseudodifferential Operators, Comm. Pure Appl. Math. 58 (2) (2005) 217-284. | MR 2094851 | Zbl 1078.35143

[13] Koch H., Tataru D., A Priori Bounds for the 1D Cubic NLS in Negative Sobolev Spaces, Internat. Math. Res. Notices 2007 (2007), article ID rnm053, 36 pages. | MR 2353092 | Zbl 1169.35055

[14] Martel Y., Merle F., Asymptotic Stability of Solitons of the Subcritical GKdV Equations Revisited, Nonlinearity 18 (1) (2005) 55-80. | MR 2109467 | Zbl 1064.35171

[15] Peetre J., New Thoughts on Besov Spaces, Duke University Mathematics Series. I, Mathematics Department, Duke University, Durham, 1976, 305 p. | MR 461123 | Zbl 0356.46038

[16] F. Rousset, N. Tzvetkov, Transverse nonlinear instability for two-dimensional dispersive models, Ann. I. H. Poincaré - AN (2008), in press, doi: 10.1016/j.anihpc.2007.09.006. | Numdam | MR 2504040 | Zbl 1169.35374

[17] Saut J.-C., Remarks on the Generalized Kadomtsev-Petviashvili Equations, Indiana Univ. Math. J. 42 (3) (1993) 1011-1026. | MR 1254130 | Zbl 0814.35119

[18] Schul'Man E. I., Zakharov V. E., Degenerative Dispersion Laws, Motion Invariants and Kinetic Equations, Physica D 1 (2) (1980) 192-202. | MR 581350

[19] Takaoka H., Well-Posedness for the Kadomtsev-Petviashvili II Equation, Adv. Differential Equations 5 (10-12) (2000) 1421-1443. | MR 1785680 | Zbl 0994.35108

[20] Takaoka H., Tzvetkov N., On the Local Regularity of the Kadomtsev-Petviashvili-II Equation, Internat. Math. Res. Notices 2001 (2) (2001) 77-114. | MR 1810481 | Zbl 0977.35126

[21] Tao T., Scattering for the Quartic Generalised Korteweg-De Vries Equation, J. Differential Equations 232 (2) (2007) 623-651. | MR 2286393 | Zbl 1171.35107

[22] Tzvetkov N., On the Cauchy Problem for Kadomtsev-Petviashvili Equation, Comm. Partial Differential Equations 24 (7-8) (1999) 1367-1397. | MR 1697491 | Zbl 0934.35161

[23] Ukai S., Local Solutions of the Kadomtsev-Petviashvili Equation, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 36 (2) (1989) 193-209. | MR 1014996 | Zbl 0703.35155

[24] Wiener N., The Quadratic Variation of a Function and Its Fourier Coefficients, in: Masani P. R. (Ed.), Collected Works With Commentaries. Volume II: Generalized Harmonic Analysis and Tauberian Theory; Classical Harmonic and Complex Analysis, Mathematicians of Our Time, vol. 15, The MIT Press, Cambridge, MA - London, 1979, (1924), XIII, 969 p. | MR 554238 | Zbl 0557.01016