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On radial solutions of semi-relativistic Hartree equations

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83942

Title: On radial solutions of semi-relativistic Hartree equations
Authors: Cho, Yonggeun Browse this author
Ozawa, Tohru Browse this author
Keywords: semi-relativistic Hartree type equation
global well-posedness
radially symmetric solution
Issue Date: 2006
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 792
Start Page: 1
End Page: 10
Abstract: We consider the semi-relativistic Hartree type equation with nonlocal nonlinearity $F(u) = \lambda (|x|^{-\gamma} * |u|^2)u, 0 < \gamma < n, n \ge 1$. In \cite{chooz2}, the global well-posedness (GWP) was shown for the value of $\gamma \in (0, \frac{2n}{n+1}), n \ge 2$ with large data and $\gamma \in (2, n), n \ge 3$ with small data. In this paper, we extend the previous GWP result to the case for $\gamma \in (1, \frac{2n-1}n), n \ge 2$ with radially symmetric large data. Solutions in a weighted Sobolev space are also studied.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69600
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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