Well-posedness and ill-posedness results for the Kadomtsev-Petviashvili-I equation
Molinet, L. ; Saut, J.-C. ; Tzvetkov, N.
Duke Math. J., Tome 115 (2002) no. 1, p. 353-384 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
The main results of this paper are concerned with the "bad" behavior of the KP-I equation with respect to a Picard iteration scheme applied to the associated integral equation, for data in usual or anisotropic Sobolev spaces. This leads to some kind of ill-posedness of the corresponding Cauchy problem: the flow map cannot be of class $C\sp 2$ in any Sobolev space.
Publié le : 2002-11-01
Classification:  35Q53,  35B30,  35R25 
@article{1085598146,
     author = {Molinet, L. and Saut, J.-C. and Tzvetkov, N.},
     title = {Well-posedness and ill-posedness results for the Kadomtsev-Petviashvili-I equation},
     journal = {Duke Math. J.},
     volume = {115},
     number = {1},
     year = {2002},
     pages = { 353-384},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1085598146}
}

Molinet, L.; Saut, J.-C.; Tzvetkov, N. Well-posedness and ill-posedness results for the Kadomtsev-Petviashvili-I equation. Duke Math. J., Tome 115 (2002) no. 1, pp.  353-384. http://gdmltest.u-ga.fr/item/1085598146/