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arXiv · 2212.08828

Global well-posedness for radial extremal hypersurface equation in $\left(1+3 \right)$-dimensional Minkowski space-time in critical Sobolev space

Sheng Wang·Yi Zhou
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Abstract

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.

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Sheng Wang, Yi Zhou. 2022-12-17. Global well-posedness for radial extremal hypersurface equation in $\left(1+3 \right)$-dimensional Minkowski space-time in critical Sobolev space. https://arxiv.org/abs/2212.08828

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