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# On radial solutions of semi-relativistic Hartree equations

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 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