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

J. Colliander; A. D. Ionescu; C. E. Kenig; Gigliola Staffilani

doi:10.3934/dcds.2008.20.219

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2008, Volume 20, Issue 2: 219-258. Doi: 10.3934/dcds.2008.20.219

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

1.
Department of Mathematics University of Toronto, 100 St. George St, Room 4072 Toronto, Ontario M5S 3G3
2.
Department of Mathematics University of Wisconsin – Madison, 480 Lincoln Drive Madison, WI 53706
3.
Department of Mathematics, University of Chicago, IL 60637
4.
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139-4307

Received: April 30, 2007

Revised: September 30, 2007

Published: April 2008

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Abstract

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.

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Mathematics Subject Classification: 35Q53, 37K10, 42B35.

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