Maximal function estimates with applications to a modified Kadomstev-Petviashvili equation
C. E. Kenig S. N. Ziesler
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
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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