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

Yanfang Gao; Zhiyong Wang

doi:10.3934/dcds.2017084

Article Contents

2017, Volume 37, Issue 4: 1979-2007. Doi: 10.3934/dcds.2017084

This issue Previous Article Almost automorphic delayed differential equations and Lasota-Wazewska model Next Article A unified approach to weighted Hardy type inequalities on Carnot groups

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

Yanfang Gao^1, and
Zhiyong Wang^1, ,

1.
Department of Mathematics, Fujian Provincial Key Laboratory of Mathematical Analysis and its Applications, Fujian Normal University, Fuzhou, 350007, China

* Corresponding author
* Corresponding author

Received: February 29, 2016

Revised: October 31, 2016

Published: May 2017

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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Abstract

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.

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Mathematics Subject Classification: Primary:35Q55.

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