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- W2994766364 abstract "The global well-posedness for the KP-Ⅱ equation is established in the anisotropic Sobolev space begin{document}$ H^{s, 0} $end{document} for begin{document}$ s>-frac{3}{8} $end{document} . Even though conservation laws are invalid in the Sobolev space with negative index, we explore the asymptotic behavior of the solution by the aid of the begin{document}$ I $end{document} -method in which Colliander, Keel, Staffilani, Takaoka, and Tao introduced a series of modified energy terms. Moreover, a-priori estimate of the solution leads to the existence of global attractor for the weakly damped, forced KP-Ⅱ equation in the weak topology of the Sobolev space when begin{document}$ s>-frac{1}{8} $end{document} ." @default.
- W2994766364 created "2019-12-26" @default.
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- W2994766364 date "2020-01-01" @default.
- W2994766364 modified "2023-09-25" @default.
- W2994766364 title "Global well-posedness and existence of the global attractor for the Kadomtsev-Petviashvili Ⅱ equation in the anisotropic Sobolev space" @default.
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- W2994766364 doi "https://doi.org/10.3934/dcds.2020078" @default.
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