In this paper, we study the fifth order Kadomtsev–Petviashvili II (KP–II) equation on the upper half–plane $U=\{(x,y)\in \mathbb R^2: y>0\}$. 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.

中文翻译：

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上半平面上的五阶KP–II方程

在本文中，我们研究了上半平面$ U = \ {（x，y）\ in \ mathbb R ^ 2：y> 0 \} $中的五阶Kadomtsev–Petviashvili II（KP–II）方程。尤其是，我们使用Bourgain的受限范数方法和求解初始值和边值问题的傅里叶-拉普拉斯方法，获得了低规则性的局部适定性。此外，我们证明了该解的非线性部分比初始数据更平滑。