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May  2008, 20(2): 219-258. doi: 10.3934/dcds.2008.20.219

Weighted low-regularity solutions of the KP-I initial-value problem

J. Colliander 1, , A. D. Ionescu 2, , C. E. Kenig 3, and  Gigliola Staffilani 4,

1. 

Department of Mathematics University of Toronto, 100 St. George St, Room 4072 Toronto, Ontario M5S 3G3, Canada
2. 

Department of Mathematics University of Wisconsin – Madison, 480 Lincoln Drive Madison, WI 53706, United States
3. 

Department of Mathematics, University of Chicago, IL 60637, United States
4. 

Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139-4307

Received  May 2007 Revised  October 2007 Published  November 2007

In this paper we correct the proofs of some statements that Colliander, Kenig and Staffilani made for the KP-I initial-value problem in [2]. These corrections actually give stronger well-posedness results than the one claimed in the above mentioned paper. The new proofs are inspired by those used by Ionescu-Kenig ([3, 4, 5]) in works on the Benjamin-Ono equation and on the Schrödinger map problems.
Keywords: KP-I equation, dispersion function., well-posedness.
Mathematics Subject Classification: 35Q53, 37K10, 42B3.
Citation: J. Colliander, A. D. Ionescu, C. E. Kenig, Gigliola Staffilani. Weighted low-regularity solutions of the KP-I initial-value problem. Discrete and Continuous Dynamical Systems, 2008, 20 (2) : 219-258. doi: 10.3934/dcds.2008.20.219
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