A Finsler type Lipschitz optimal transport metric for a quasilinear wave equation

Hong Cai; Geng Chen; Yannan Shen

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arXiv · 2007.15201

A Finsler type Lipschitz optimal transport metric for a quasilinear wave equation

Hong Cai·Geng Chen·Yannan Shen

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Abstract

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.

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Hong Cai, Geng Chen, Yannan Shen. 2020-07-30. A Finsler type Lipschitz optimal transport metric for a quasilinear wave equation. https://arxiv.org/abs/2007.15201

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