论文标题
产品空间上的3D quasilinear klein-gordon方程的几乎全局平滑解决方案$ \ mathbb {r}^{2} {2} \ times \ times \ mathbb {t} $
Almost global smooth solutions of the 3D quasilinear Klein-Gordon equations on the product space $\mathbb{R}^{2}\times \mathbb{T}$
论文作者
论文摘要
在本文中，对于3D Quasilinear klein-gordon方程，带有较小的初始数据在产品空间上$ \ mathbb {r}^{2} {2} \ times \ times \ mathbb {t} $，我们专注于光滑解决方案寿命的下限。 When the size of initial data is bounded by $\varepsilon_0>0$, by the space-time resonance method, it is shown that smooth solution exists up to the time $e^{c_{0}/\varepsilon_{0}^2}$ with $\varepsilon_0$ being sufficiently small and $c_0>0$ being some suitable constant.
In the paper, for the 3D quasilinear Klein-Gordon equation with the small initial data posed on the product space $\mathbb{R}^{2}\times \mathbb{T}$, we focus on the lower bound of the lifespan of the smooth solution. When the size of initial data is bounded by $\varepsilon_0>0$, by the space-time resonance method, it is shown that smooth solution exists up to the time $e^{c_{0}/\varepsilon_{0}^2}$ with $\varepsilon_0$ being sufficiently small and $c_0>0$ being some suitable constant.
