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- W2901921623 abstract "Abstract This paper is concerned with the Cauchy problem for the Hartree equation on R n , n ∈ N with the nonlinearity of type ( | ⋅ | − γ ⁎ | u | 2 ) u , 0 γ n . It is shown that a global solution with some twisted persistence property exists for data in the space L p ∩ L 2 , 1 ≤ p ≤ 2 under some suitable conditions on γ and spatial dimension n ∈ N . It is also shown that the global solution u has a smoothing effect in terms of spatial integrability in the sense that the map t ↦ u ( t ) is well defined and continuous from R ∖ { 0 } to L p ′ , which is well known for the solution to the corresponding linear Schrodinger equation. Local and global well-posedness results for hat L p -spaces are also presented. The local and global results are proved by combining arguments by Carles–Mouzaoui with a new functional framework introduced by Zhou. Furthermore, it is also shown that the global results can be improved via generalized dispersive estimates in the case of one space dimension." @default.
- W2901921623 created "2018-11-29" @default.
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- W2901921623 date "2019-07-01" @default.
- W2901921623 modified "2023-09-24" @default.
- W2901921623 title "On the global Cauchy problem for the Hartree equation with rapidly decaying initial data" @default.
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- W2901921623 doi "https://doi.org/10.1016/j.anihpc.2018.11.004" @default.
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