The fifth order KP-II equation on the upper half-plane
Differential and Integral Equations, cilt.33, sa.12, ss.555-596, 2020 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 33 Sayı: 12
- Basım Tarihi: 2020
- Dergi Adı: Differential and Integral Equations
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
- Sayfa Sayıları: ss.555-596
- Boğaziçi Üniversitesi Adresli: Evet
Özet
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.