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

2019/03/08 by Erdogan, M. B., Gurel, T. B., Tzirakis, N.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.03580

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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