Almost global smooth solutions of the 3D quasilinear Klein-Gordon equations on the product space ℝ²× \mathbbT

2022/04/18 by Li, Jun, Tao, Fei, Yin, Huicheng
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2204.08130

Abstract

In the paper, for the 3D quasilinear Klein-Gordon equation with the small initial data posed on the product space ℝ²× \mathbbT, we focus on the lower bound of the lifespan of the smooth solution. When the size of initial data is bounded by ε₀>0, by the space-time resonance method, it is shown that smooth solution exists up to the time e^c₀/ε₀² with ε₀ being sufficiently small and c₀>0 being some suitable constant.

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