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

被引:5
作者
Cai, Hong [1 ,2 ]
Chen, Geng [3 ]
Shen, Yannan [3 ]
机构
[1] Qingdao Univ Sci & Technol, Dept Math, Qingdao 266061, Shandong, Peoples R China
[2] Qingdao Univ Sci & Technol, Res Inst Math & Interdisciplinary Sci, Qingdao 266061, Shandong, Peoples R China
[3] Univ Kansas, Dept Math, Lawrence, KS 66045 USA
基金
中国国家自然科学基金;
关键词
Variational wave equations; Generic regularity; Lipschitz metric; Optimal transport; Conservative solutions; CONSERVATIVE SOLUTIONS; SINGULARITIES;
D O I
10.1016/j.jde.2023.01.035
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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. (c) 2023 Elsevier Inc. All rights reserved.
引用
收藏
页码:289 / 335
页数:47
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