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

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-compactnes...

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Bibliographic Details
Published inVietnam journal of mathematics Vol. 51; no. 4; pp. 869 - 909
Main Authors Cheng, Xing, Guo, Zihua, Masaki, Satoshi
Format Journal Article
LanguageEnglish
Published Singapore Springer Nature Singapore 01.10.2023
Springer Nature B.V
Subjects
Defocusing
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinearity
Original Article
Scattering
Schrodinger equation
Profile decomposition
35L71
Scattering
35P25
35B40
35Q40
Klein–Gordon equations
Well-posedness
Large scale profile
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Summary: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.
ISSN:2305-221X
2305-2228
DOI:10.1007/s10013-023-00616-4