论文标题
$ \左（1+3 \右）$ dimensional minkowski时空的全球径向极端超出表方程
Global well-posedness for radial extremal hypersurface equation in $\left(1+3 \right)$-dimensional Minkowski space-time in critical Sobolev space
论文作者
论文摘要
在本文中，我们证明了在关键的Sobolev空间中的全球范围，$ h_ {rad}^2 \ left（\ Mathbb {r}^2 \ right）\ times h_ {rad}^1 \ left（\ mathbb {r}^r}^2 \右） Minkowski时空。这是通过推导新的Div-Curl型引理来实现的，并将其与能量和``动量''平衡法相结合，以获得对非线性的一些时空估计。
In this article, we prove the global well-posedness in the critical Sobolev space $H_{rad}^2\left(\mathbb{R}^2\right) \times H_{rad}^1 \left(\mathbb{R}^2\right)$ for the radial time-like extremal hypersurface equation in $\left(1+3\right)$- dimensional Minkowski space-time. This is achieved by deriving a new div-curl type lemma and combined it with energy and ``momentum" balance law to get some space-time estimates of the nonlinearity.
