The fifth order KP–II equation on the upper half–plane
The fifth order KP–II equation on the upper half–plane
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 …