Abstract
We consider the asymptotic behavior of solutions to the Cauchy problem for the defocusing nonlinear Klein–Gordon equation (NLKG) with exponential nonlinearity in the one spatial dimension with data in the energy space [Formula: see text]. We prove that any energy solution has a global bound of the [Formula: see text] space-time norm, and hence, scatters in [Formula: see text] as [Formula: see text]. The proof is based on the argument by Killip–Stovall–Visan (Trans. Amer. Math. Soc. 364(3) (2012) 1571–1631). However, since well-posedness in [Formula: see text] for NLKG with the exponential nonlinearity holds only for small initial data, we use the [Formula: see text]-norm for some [Formula: see text] instead of the [Formula: see text]-norm, where [Formula: see text] denotes the [Formula: see text]th order [Formula: see text]-based Sobolev space.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
