{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,9]],"date-time":"2026-02-09T23:35:22Z","timestamp":1770680122865,"version":"3.49.0"},"reference-count":36,"publisher":"IOP Publishing","issue":"5","license":[{"start":{"date-parts":[[2021,5,7]],"date-time":"2021-05-07T00:00:00Z","timestamp":1620345600000},"content-version":"vor","delay-in-days":6,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/iop-standard\/v1"},{"start":{"date-parts":[[2021,5,7]],"date-time":"2021-05-07T00:00:00Z","timestamp":1620345600000},"content-version":"tdm","delay-in-days":6,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","award":["UID\/MAT\/04561\/2019"],"award-info":[{"award-number":["UID\/MAT\/04561\/2019"]}]},{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"crossref","award":["19-11-00069"],"award-info":[{"award-number":["19-11-00069"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100004561","name":"Ministry of Education and Science of the Republic of Kazakhstan","doi-asserted-by":"crossref","award":["AP08052425"],"award-info":[{"award-number":["AP08052425"]}],"id":[{"id":"10.13039\/501100004561","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Nonlinearity"],"published-print":{"date-parts":[[2021,5,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    The classical Kelvin\u2013Voigt equations for incompressible fluids with non-constant density are investigated in this work. To the associated initial-value problem endowed with zero Dirichlet conditions on the assumed Lipschitz-continuous boundary, we prove the existence of weak solutions: velocity and density. We also prove the existence of a unique pressure. These results are valid for\n                    <jats:italic>d<\/jats:italic>\n                    \u2208 {2, 3, 4}. In particular, if\n                    <jats:italic>d<\/jats:italic>\n                    \u2208 {2, 3}, the regularity of the velocity and density is improved so that their uniqueness can be shown. In particular, the dependence of the regularity of the solutions on the smoothness of the given data of the problem is established.\n                  <\/jats:p>","DOI":"10.1088\/1361-6544\/abe51e","type":"journal-article","created":{"date-parts":[[2021,5,12]],"date-time":"2021-05-12T09:38:13Z","timestamp":1620812293000},"page":"3083-3111","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":24,"title":["The classical Kelvin\u2013Voigt problem for incompressible fluids with unknown non-constant density: existence, uniqueness and regularity"],"prefix":"10.1088","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9469-9902","authenticated-orcid":false,"given":"S N","family":"Antontsev","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9053-8442","authenticated-orcid":false,"given":"H B","family":"de Oliveira","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5525-111X","authenticated-orcid":false,"given":"Kh","family":"Khompysh","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2021,5,7]]},"reference":[{"key":"nonabe51ebib1","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2020.111790","type":"journal-article","article-title":"Turbulent flows as generalized Kelvin\u2013Voigt materials: modeling and analysis","volume":"196","author":"Amrouche","year":"2020","journal-title":"Nonlinear Anal."},{"key":"nonabe51ebib2","author":"Antontsev","year":"1990","type":"book"},{"key":"nonabe51ebib3","doi-asserted-by":"publisher","first-page":"1255","DOI":"10.1016\/j.jmaa.2016.09.023","type":"journal-article","article-title":"Kelvin\u2013Voigt equation with p-Laplacian and damping term: existence, uniqueness and blow-up","volume":"446","author":"Antontsev","year":"2017","journal-title":"J. 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All rights, including for text and data mining, AI training, and similar technologies, are reserved.","name":"copyright_information","label":"Copyright Information"},{"value":"2020-07-24","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2021-02-10","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2021-05-07","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}