{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:29:49Z","timestamp":1787318989045,"version":"build-2736575974"},"reference-count":29,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Math. Anal."],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>Motivated by lubrication problems, we consider a micropolar fluid flow in a two-dimensional domain with a rough and free boundary. We assume that the thickness and the roughness are both of order $0&lt;\\varepsilon \\ll 1$. We prove the existence and uniqueness of a solution of this problem for any value of $\\varepsilon$, and we establish some a priori estimates. Then we use the two-scale convergence technique to derive the limit problem when $\\varepsilon$ tends to zero. Moreover we show that the limit velocity and microrotation fields are uniquely determined via auxiliary well-posed problems and the limit pressure is given as the unique solution of a Reynolds equation.<\/jats:p>","DOI":"10.1137\/110837772","type":"journal-article","created":{"date-parts":[[2012,4,24]],"date-time":"2012-04-24T20:38:12Z","timestamp":1335299892000},"page":"1211-1256","source":"Crossref","is-referenced-by-count":17,"title":["Asymptotic Analysis of a Micropolar Fluid Flow in a Thin Domain with a Free and Rough Boundary"],"prefix":"10.1137","volume":"44","author":[{"given":"Mahdi","family":"Boukrouche","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Laetitia","family":"Paoli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,4,24]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/0523084"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-7225(73)90038-4"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/0020-7225(74)90059-7"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2010.04.040"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2005.07.007"},{"key":"R6","first-page":"81","volume":"309","author":"Bayada M.","year":"1989","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. I Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0764-4442","issn-type":"print"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1090\/S0033-569X-05-00963-3"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1002\/mma.630"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1090\/S0033-569X-06-01030-3"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2005.06.018"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1016\/j.crme.2005.04.006"},{"key":"R12","unstructured":"G. Duvaut and J.L. Lions,\n                      Les In\u00e9quations en M\u00e9canique et en Physique\n                      , Dunod, Paris, 1972."},{"key":"R13","first-page":"1","volume":"16","author":"Eringen A.C.","year":"1966","journal-title":"J. Math. Mech.","ISSN":"https:\/\/id.crossref.org\/issn\/0095-9057","issn-type":"print"},{"key":"R14","doi-asserted-by":"crossref","unstructured":"A.C. Eringen,\n                      Microcontinuum Field Theories.\n                      I.\n                      Foundations and Solids\n                      , Springer-Verlag, New York, 1999.","DOI":"10.1007\/978-1-4612-0555-5"},{"key":"R15","doi-asserted-by":"crossref","unstructured":"C. Foias, O. Manley, R. Rosa, and R. Temam,\n                      Navier-Stokes Equations and Turbulence\n                      , Encyclopedia Math. Appl. 83, Cambridge University Press, Cambridge, UK, 2001.","DOI":"10.1017\/CBO9780511546754"},{"key":"R16","doi-asserted-by":"crossref","unstructured":"G.P. Galdi,\n                      An Introduction to the Navier-Stokes Initial-Boundary Value Problem\n                      , http:\/\/ numerik.iwr.uni-heidelberg.de\/Oberwolfach-Seminar\/Galdi_Navier_Stokes_Notes.pdf (2000).","DOI":"10.1007\/978-3-0348-8424-2_1"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(00)85011-7"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1023\/A:1023049608047"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1002\/mma.1303"},{"key":"R20","doi-asserted-by":"crossref","first-page":"583","DOI":"10.3934\/cpaa.2011.10.583","volume":"10","author":"Jinbo G.","year":"2011","journal-title":"Commun. Pure Appl. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/1534-0392","issn-type":"print"},{"key":"R21","unstructured":"J.L. Lions,\n                      Some problems connected with Navier-Stokes equations\n                      , in 4th Latin-American School of Mathematics (Lima, Peru, 1978), ELAM, Lima, Peru, 1979, pp. 222\u2013286."},{"key":"R22","doi-asserted-by":"crossref","unstructured":"G. \u0141ukaszewicz,\n                      Micropolar Fluids. Theory and Applications, Modeling and Simulation in Science, Engineering and Technology\n                      , Birkh\u00e4user, Boston, Basel, Berlin, 1999.","DOI":"10.1007\/978-1-4612-0641-5"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1016\/S0895-7177(01)00078-4"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.1995.1.485"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1137\/0520043"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.3233\/BIR-1974-11605"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1007\/s000210050010"},{"key":"R28","unstructured":"R. Temam,\n                      Navier-Stokes Equations. Theory and Numerical Analysis\n                      , North\u2013Holland, Amsterdam, 1979."},{"key":"R29","doi-asserted-by":"crossref","first-page":"257","DOI":"10.3233\/ASY-2000-398","volume":"23","author":"Wright S.","year":"2000","journal-title":"Asymptot. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0921-7134","issn-type":"print"}],"container-title":["SIAM Journal on Mathematical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/110837772","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:44:09Z","timestamp":1787316249000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/110837772"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":29,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1137\/110837772"],"URL":"https:\/\/doi.org\/10.1137\/110837772","relation":{},"ISSN":["0036-1410","1095-7154"],"issn-type":[{"value":"0036-1410","type":"print"},{"value":"1095-7154","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,1]]}}}