Global existence of smooth solution to 2D relativistic membrane equation in asymptotically flat FLRW space‐time
Global existence of smooth solution to 2D relativistic membrane equation in asymptotically flat FLRW space‐time
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DOI：
10.1002/mma.5610
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发表时间：
2019-04
影响因子：
2.9
通讯作者：
Changhua Wei
中科院分区：
文献类型：
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作者：
Changhua Wei
本文研究了弯曲时空中演化的二维相对论性膜方程，其度规被描述为对平坦的系数依赖于时间的Friedmann-Lemaittre-Robertson-步行者（FLRW）度规的小扰动.由于膜方程的部分“零结构”和背景度量的性质，我们可以通过加权能量估计证明一类时间依赖解的全局稳定性.
This paper is concerned with the 2D relativistic membrane equation evolving in curved space‐time, whose metric is prescribed as a small perturbation to the flat Friedmann‐Lemaître‐Robertson‐Walker (FLRW) metric with time‐dependent coefficients. Thanks to the partial “null structure” of the membrane equation and the properties of the background metric, we could prove the global stability of a class of time‐dependent solutions by weighted energy estimate.