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Constrained minimization problem and unbounded dynamics for the four-dimensional Klein-Gordon-Schrödinger System

  • Masaru Hamano
  • Hiroaki Kikuchi
  • Kenta Tomioka
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Abstract

In this paper, we study the Klein-Gordon-Schrodinger system in four spatial dimensions. We consider a constrained minimization problem associated with the corresponding stationary system and establish the existence of a positive radial minimizer. We further investigate the asymptotic behavior and qualitative properties of minimizers. As an application, we analyze the dynamics of solutions with initial data in a potential well and prove that such solutions either blow up in finite time or exhibit unbounded growth in the energy norm as time tends to infinity. Since the minimizers lie on the boundary of the potential well, we also establish the strong instability of the associated standing waves.

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Cite

BibTeXRIS
BibTeX
@misc{hamano2026constrained,
  title = {{Constrained minimization problem and unbounded dynamics for the four-dimensional Klein-Gordon-Schrödinger System}},
  author = {Masaru Hamano and Hiroaki Kikuchi and Kenta Tomioka},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.06094},
  eprint = {2611.06094},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.06094},
}
RIS
TY  - UNPB
TI  - Constrained minimization problem and unbounded dynamics for the four-dimensional Klein-Gordon-Schrödinger System
AU  - Masaru Hamano
AU  - Hiroaki Kikuchi
AU  - Kenta Tomioka
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.06094
UR  - https://arxiv.org/abs/2611.06094
AB  - In this paper, we study the Klein-Gordon-Schrodinger system in four spatial dimensions. We consider a constrained minimization problem associated with the corresponding stationary system and establish the existence of a positive radial minimizer. We further investigate the asymptotic behavior and qualitative properties of minimizers. As an application, we analyze the dynamics of solutions with initial data in a potential well and prove that such solutions either blow up in finite time or exhibit unbounded growth in the energy norm as time tends to infinity. Since the minimizers lie on the boundary of the potential well, we also establish the strong instability of the associated standing waves.
ER  -