On the local regularity of the Kadomtsev-Petviashvili-II equation

By Hideo Takaoka, N. Tzvetkov. 2001

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Global well-posedness of the KP-I initial-value problem in the energy space (2007, background): “The KP-II equation is well understood from the point of view of well-posedness: the KP-II initial-value problem is globally well-posed for suitable data in L(2), on both R(2) and T(2) = S(1) × S(1), see [4], as well as in some spaces larger than L(2), see [18] and the references therein.”
Well-posedness and ill-posedness results for the Kadomtsev-Petviashvili-I equation (2002, background): “The regions R 1 , R 2 , and R 3 can be handled similarly to [25] in the case of the KP-II equation since for (τ, ζ, τ 1 , ζ 1 ) ∈ R 1 ∪ R 2 ∪ R 3 one has a lower bound for the quantity max τ 1 − ξ 3 1 − η 2 1 ξ 1 , (τ − τ 1 ) − (ξ − ξ 1 ) 3 − (η − η 1 ) 2 ξ − ξ 1 , τ − ξ 3 − η 2 ξ .”
Well-posedness and scattering for the KP-II equation in a critical space (2007, background): “3 (this is implicitly contained in the earlier work [20]).”
Well-posedness for the Kadomtsev-Petviashvili II equation and generalisations (2006, methodology): “[16] H. Takaoka and N. Tzvetkov.”
Almost conservation laws and global rough solutions to a Nonlinear Schr (2002, unknown): “(See [3], [7], [13], [18], [22], and [23]).”