Scattering for the Mass-Critical Nonlinear Klein–Gordon Equations in Three and Higher Dimensions

Xing Cheng, Zihua Guo, Satoshi Masaki

Research output: Contribution to journalArticleResearchpeer-review

Abstract

In this paper we consider the mass-critical nonlinear Klein–Gordon equations in three and higher dimensions. We prove the dichotomy between scattering and blow-up below the ground state energy in the focusing case, and the energy scattering in the defocusing case. We use the concentration-compactness/rigidity method developed by C. E. Kenig and F. Merle. The main novelty from the work of R. Killip, B. Stovall, and M. Visan (Trans. Amer. Math. Soc. 364, 2012) is to approximate the large scale (low-frequency) profile by the solution of the mass-critical nonlinear Schrödinger equation when the nonlinearity is not algebraic.

Original languageEnglish
Pages (from-to)869-909
Number of pages41
JournalVietnam Journal of Mathematics
Volume51
Issue number4
DOIs
Publication statusPublished - Oct 2023

Keywords

  • Klein–Gordon equations
  • Large scale profile
  • Profile decomposition
  • Scattering
  • Well-posedness

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