Global solution for the Kadomtsev-Petviashvili equation (KPII) in anisotropic Sobolev spaces of negative indices
Date
2003-06-13
Authors
Isaza J., Pedro
Mejia L., Jorge
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
It is proved that the Cauchy problem for the Kadomtsev-Petviashvili equation (KPII) is globally well-posed for initial data in anisotropic Sobolev spaces Hs0 (ℝ2) with s > -1/14. The extension of a local solution to a solution in an arbitrary interval is carried out by means of an almost conservation property of the Hs0 norm of the solution.
Description
Keywords
Nonlinear dispersive equations, Global solutions, Almost conservation laws
Citation
Isaza J., P., & Mejia L., J. (2003). Global solution for the Kadomtsev-Petviashvili equation (KPII) in anisotropic Sobolev spaces of negative indices. <i>Electronic Journal of Differential Equations, 2003</i>(68), pp. 1-12.
Rights
Attribution 4.0 International