Minimal mass non-scattering solutions of the focusing <i>L</i><sup>2</sup>-critical Hartree equations with radial data

Abstract

Listen

Translate article

We prove that for the Cauchy problem of focusing \begin{document}$L^2$\end{document} -critical Hartree equations with spherically symmetric \begin{document}$H^1$\end{document} data in dimensions \begin{document}$3$\end{document} and \begin{document}$4$\end{document} , the global non-scattering solution with ground state mass must be a solitary wave up to symmetries of the equation. The approach is a linearization analysis around the ground state combined with an in-out spherical wave decomposition technique.