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arXiv · 1903.03580

The Fifth Order KP--II Equation on the Upper Half--plane

M. B. Erdogan·T. B. Gurel·N. Tzirakis
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Abstract

In this paper we study the fifth order Kadomtsev--Petviashvili II (KP--II) equation on the upper half-plane $U=\{(x,y)\in \R^2: y>0\}$. 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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M. B. Erdogan, T. B. Gurel, N. Tzirakis. 2019-03-08. The Fifth Order KP--II Equation on the Upper Half--plane. https://arxiv.org/abs/1903.03580

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