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Minimal mass non-scattering solutions of the focusing L2-critical Hartree equations with radial data

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    * Corresponding author
Both authors are supported by NFSC (Grant no.11501111), and the first author is partially supported by the program Nonlinear Analysis and Its Applications(IRTL1206) from Fujian Normal University.
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  • We prove that for the Cauchy problem of focusing $L^2$-critical Hartree equations with spherically symmetric $H^1$ data in dimensions $3$ and $4$, 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.

    Mathematics Subject Classification: Primary:35Q55.


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