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On global smooth small data solutions of 3-D quasilinear Klein-Gordon equations on $ \mathbb{R}^{2}\times \mathbb{T} $
In this paper, for the small initial data in the suitably weighted Sobolev spaces on the product space $ \mathbb{R}^2\times\mathbb{T} $, we establish the global existence of smooth solutions to the 3-D quasilinear Klein-Gordon equations with quadratic nonlinearities. It is noted that the topic on the well-posedness of the nonlinear …