Maximal function estimates with applications to a modified Kadomstev-Petviashvili equation
C. E. Kenig S. N. Ziesler
Communications on Pure & Applied Analysis 2005, 4(1): 45-91 doi: 10.3934/cpaa.2005.4.45
In this paper we give optimal (up to endpoint) maximal function type estimates for the solution of the linear initial value problem associated with the Kadomstev-Petviashvili I equation. These estimates enable us to obtain a well-posedness result for a modified Kadomstev-Petviashvili I equation.
keywords: Kadomstev-Petviashvili. maximal function estimates
Weighted low-regularity solutions of the KP-I initial-value problem
J. Colliander A. D. Ionescu C. E. Kenig Gigliola Staffilani
Discrete & Continuous Dynamical Systems - A 2008, 20(2): 219-258 doi: 10.3934/dcds.2008.20.219
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

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