{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:49Z","timestamp":1740134569922,"version":"3.37.3"},"reference-count":29,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11101145","2012M520360","201032","GFQQ2460101710"],"award-info":[{"award-number":["11101145","2012M520360","201032","GFQQ2460101710"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["11101145","2012M520360","201032","GFQQ2460101710"],"award-info":[{"award-number":["11101145","2012M520360","201032","GFQQ2460101710"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Doctoral Foundation of North China University of Water Sources and Electric Power","award":["11101145","2012M520360","201032","GFQQ2460101710"],"award-info":[{"award-number":["11101145","2012M520360","201032","GFQQ2460101710"]}]},{"DOI":"10.13039\/501100013057","name":"Innovation Scientists and Technicians Troop Construction Projects of Henan Province","doi-asserted-by":"crossref","award":["11101145","2012M520360","201032","GFQQ2460101710"],"award-info":[{"award-number":["11101145","2012M520360","201032","GFQQ2460101710"]}],"id":[{"id":"10.13039\/501100013057","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["11101145","2012M520360","201032","GFQQ2460101710"],"award-info":[{"award-number":["11101145","2012M520360","201032","GFQQ2460101710"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>We study the free boundary value problem for one-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficient and discontinuous initial data in this paper. For piecewise regular initial density, we show that there exists a unique global piecewise regular solution, the interface separating the flow and vacuum state propagates along particle path and expands outwards at an algebraic time-rate, the flow density is strictly positive from blow for any finite time and decays pointwise to zero at an algebraic time-rate, and the jump discontinuity of density also decays at an algebraic time-rate as the time tends to infinity.<\/jats:p>","DOI":"10.1155\/2013\/505108","type":"journal-article","created":{"date-parts":[[2013,7,9]],"date-time":"2013-07-09T21:01:30Z","timestamp":1373403690000},"page":"1-11","source":"Crossref","is-referenced-by-count":0,"title":["Free Boundary Value Problem for the One-Dimensional Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Discontinuous Initial Data"],"prefix":"10.1155","volume":"2013","author":[{"given":"Ruxu","family":"Lian","sequence":"first","affiliation":[{"name":"College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450011, China"},{"name":"Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guojing","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500018953"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.2307\/2000785"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(92)90042-L"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.1992.41.41060"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1995.1111"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1007\/BF00390346"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1080\/03605300008821583"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1007\/s002050050055"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.10046"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2005.07.011"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2009.11.029"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/S0252-9602(12)60019-8"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2001.1.89"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.euromechflu.2006.04.007"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-011-1334-6"},{"issue":"3","key":"16","doi-asserted-by":"crossref","first-page":"239","DOI":"10.4310\/MAA.2005.v12.n3.a2","volume":"12","year":"2005","journal-title":"Methods and Applications of Analysis"},{"issue":"1","key":"17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3934\/dcds.1998.4.1","volume":"4","year":"1998","journal-title":"Discrete and Continuous Dynamical Systems"},{"issue":"1","key":"18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02824736","volume":"48","year":"2002","journal-title":"Annali dell'Universit\u00e0 di Ferrara Nuova 8"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-0396(03)00060-3"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1081\/PDE-100002385"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.2001.4140"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-002-0703-6"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1137\/060658199"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1137\/070680333"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1080\/03605302.2010.516785"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.3934\/krm.2008.1.313"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-008-0495-4"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0312(199803)51:3&lt;229::AID-CPA1&gt;3.3.CO;2-K"},{"issue":"3","key":"29","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/S0294-1449(16)30403-6","volume":"2","year":"1985","journal-title":"Annales de l'Institut Henri Poincar\u00e9. Analyse Non Lin\u00e9aire"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/505108.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/505108.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/505108.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,2,28]],"date-time":"2022-02-28T00:10:40Z","timestamp":1646007040000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/505108\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":29,"alternative-id":["505108","505108"],"URL":"https:\/\/doi.org\/10.1155\/2013\/505108","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}