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Math. Anal."],"published-print":{"date-parts":[[2024,8,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this paper, we study the Lipschitz continuous dependence of conservative H\u00f6lder continuous weak solutions to a variational wave system derived from a model for nematic liquid crystals. Since the solution of this system generally forms a finite time cusp singularity, the solution flow is not Lipschitz continuous under the Sobolev metric used in the existence and uniqueness theory. We establish a Finsler type optimal transport metric, and show the Lipschitz continuous dependence of the solution on the initial data under this metric. This kind of Finsler type optimal transport metrics was first established in [A. Bressan and G. Chen, Arch. Ration. Mech. Anal., 226 (2017), pp. 1303-1343] for the scalar variational wave equation. This equation can be used to describe the unit direction [Formula: see text] of mean orientation of nematic liquid crystals, when [Formula: see text] is restricted on a circle. The model considered in this paper describes the propagation of [Formula: see text] without this restriction, i.e. [Formula: see text], takes any value on the unit sphere. So we need to consider a wave system instead of a scalar equation.<\/jats:p>","DOI":"10.1137\/24m1629547","type":"journal-article","created":{"date-parts":[[2024,7,16]],"date-time":"2024-07-16T04:04:01Z","timestamp":1721102641000},"page":"5144-5174","source":"Crossref","is-referenced-by-count":3,"title":["Lipschitz Optimal Transport Metric for a Wave System Modeling Nematic Liquid Crystals"],"prefix":"10.1137","volume":"56","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4823-8734","authenticated-orcid":true,"given":"Hong","family":"Cai","sequence":"first","affiliation":[{"name":"Corresponding author. School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao, Shandong, 266061, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Geng","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Kansas, Lawrence, KS 66045 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yannan","family":"Shen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Kansas, Lawrence, KS 66045 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,7,16]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.3934\/krm.2009.2.1"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.anihpc.2015.12.004"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-017-1155-7"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-015-0849-y"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.4310\/CMS.2016.v14.n1.a2"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-006-0047-8"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.matpur.2018.04.002"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1063\/5.0079917"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2023.01.035"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-019-01484-4"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.3934\/cpaa.2013.12.1445"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160460705"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1063\/1.2808028"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1996.0111"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-011-0403-5"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160420605"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2013.0361"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/100\/1033527"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160410405"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160450803"},{"key":"ref21","doi-asserted-by":"crossref","DOI":"10.1090\/gsm\/058","volume-title":"Topics in Optmal Transportation","author":"Villani C.","year":"2003"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-002-0232-7"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-009-0222-0"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.20380"}],"container-title":["SIAM Journal on Mathematical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/24M1629547","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:59:14Z","timestamp":1787320754000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/24M1629547"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,16]]},"references-count":24,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,8,31]]}},"alternative-id":["10.1137\/24M1629547"],"URL":"https:\/\/doi.org\/10.1137\/24m1629547","relation":{},"ISSN":["0036-1410","1095-7154"],"issn-type":[{"value":"0036-1410","type":"print"},{"value":"1095-7154","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7,16]]}}}