The time-like minimal surface equation in Minkowski space: low regularity solutions
The time-like minimal surface equation in Minkowski space: low regularity solutions
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DOI：
10.1007/s00222-023-01231-3
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发表时间：
2021-10
影响因子：
3.1
通讯作者：
Albert Ai;M. Ifrim;D. Tataru
中科院分区：
文献类型：
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作者：
Albert Ai;M. Ifrim;D. Tataru
长期以来，人们一直猜想，对于满足零点条件的非线性形式的非线性波动方程，与Smith-Tataru在一般情况下的精确结果相比，低正则适定性理论可以得到显著的改进。本文的目的是证明这方面的第一个结果，即Minkowski时空中的类时极小曲面方程。此外，我们的改进是巨大的，即通过在两个空间维度上的导数和通过在更高维度上的导数。
It has long been conjectured that for nonlinear wave equations that satisfy a nonlinear form of the null condition, the low regularity well-posedness theory can be significantly improved compared to the sharp results of Smith-Tataru for the generic case. The aim of this article is to prove the first result in this direction, namely for the time-like minimal surface equation in the Minkowski space-time. Further, our improvement is substantial, namely byderivatives in two space dimensions and byderivatives in higher dimensions.