@article{b4be1326f1ca4c149bda5491aaed1901,

title = "The fifth order KP-II equation on the upper half-plane",

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.",

author = "Erdoğan, {M. B.} and G{\"u}rel, {T. B.} and N. Tzirakis",

note = "Funding Information: Acknowledgment. The first author is partially supported by NSF grant DMS-1501041. The second author is partially supported by T{\"U}BİTAK grant 118F152 and Bogazic¸i University Research Fund grant BAP-14081. The third author{\textquoteright}s work was supported by a grant from the Simons Foundation (#355523 Nikolaos Tzirakis) and by Illinois Campus Research Board RB 18051. The authors wishes to thank an anonymous referee for useful comments that improved the presentation of the paper. Funding Information: The first author is partially supported by NSF grant DMS-1501041. The second author is partially supported by T?B?TAK grant 118F152 and Bo?azi?i University Research Fund grant BAP-14081. The third author's work was supported by a grant from the Simons Foundation (#355523 Nikolaos Tzirakis) and by Illinois Campus Research Board RB 18051. The authors wishes to thank an anonymous referee for useful comments that improved the presentation of the paper. Publisher Copyright: {\textcopyright} 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.",

year = "2020",

month = nov,

language = "English (US)",

volume = "33",

pages = "555--596",

journal = "Differential and Integral Equations",

issn = "0893-4983",

publisher = "Khayyam Publishing, Inc.",

number = "12",

}