The fifth order KP-II equation on the upper half-plane

M. B. Erdoğan; T. B. Gürel; N. Tzirakis

The fifth order KP-II equation on the upper half-plane

Mathematics

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Abstract

In this paper, we study the fifth order Kadomtsev-Petviashvili II (KP-II) equation on the upper half-plane U = {(x, y) ∈ R² : y > 0}. In particular, we obtain low regularity local well-posedness using the restricted norm method of Bourgain and the Fourier-Laplace method of solving initial and boundary value problems. Moreover, we prove that the nonlinear part of the solution is in a smoother space than the initial data.

Original language	English (US)
Pages (from-to)	555-596
Number of pages	42
Journal	Differential and Integral Equations
Volume	33
Issue number	12
State	Published - Nov 2020

ASJC Scopus subject areas

Analysis
Applied Mathematics

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abstract = "In this paper, we study the fifth order Kadomtsev-Petviashvili II (KP-II) equation on the upper half-plane U = {(x, y) ∈ R2 : y > 0}. In particular, we obtain low regularity local well-posedness using the restricted norm method of Bourgain and the Fourier-Laplace method of solving initial and boundary value problems. Moreover, we prove that the nonlinear part of the solution is in a smoother space than the initial data.",

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AU - Gürel, T. B.

AU - Tzirakis, N.

N1 - Publisher Copyright: © Medical Communications Sp. z o.o. This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (CC BY-NC-ND). Reproduction is permitted for personal, educational, non-commercial use, provided that the original article is in whole, unmodified, and properly cited.

PY - 2020/11

Y1 - 2020/11

N2 - In this paper, we study the fifth order Kadomtsev-Petviashvili II (KP-II) equation on the upper half-plane U = {(x, y) ∈ R2 : y > 0}. In particular, we obtain low regularity local well-posedness using the restricted norm method of Bourgain and the Fourier-Laplace method of solving initial and boundary value problems. Moreover, we prove that the nonlinear part of the solution is in a smoother space than the initial data.

AB - In this paper, we study the fifth order Kadomtsev-Petviashvili II (KP-II) equation on the upper half-plane U = {(x, y) ∈ R2 : y > 0}. In particular, we obtain low regularity local well-posedness using the restricted norm method of Bourgain and the Fourier-Laplace method of solving initial and boundary value problems. Moreover, we prove that the nonlinear part of the solution is in a smoother space than the initial data.

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ER -

The fifth order KP-II equation on the upper half-plane

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