论文标题
Finsler类型Lipschitz的准电波方程式的最佳运输度量
A Finsler type Lipschitz optimal transport metric for a quasilinear wave equation
论文作者
论文摘要
我们将弱能量保守溶液的全球良好性通过变异原理对一般的准线性波动方程式进行，当能量集中时，该解决方案可能会形成有限的时间尖尖。作为本文的主要结果，我们构建了一个Finsler型最佳运输度量，然后证明解决方案流是该指标下的Lipschitz。我们还通过应用Thom的横向定理，然后在一组密集的解决方案中找到分段平滑的传输路径，从而证明了一般的规律性结果。本文的结果是针对大型数据解决方案的，而无需限制解决方案的大小。
We consider the global well-posedness of weak energy conservative solution to a general quasilinear wave equation through variational principle, where the solution may form finite time cusp singularity, when energy concentrates. As a main result in this paper, we construct a Finsler type optimal transport metric, then prove that the solution flow is Lipschitz under this metric. We also prove a generic regularity result by applying Thom's transversality theorem, then find piecewise smooth transportation paths among a dense set of solutions. The results in this paper are for large data solutions, without restriction on the size of solutions.
