{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T05:20:31Z","timestamp":1775539231079,"version":"3.50.1"},"reference-count":23,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2004,5,6]],"date-time":"2004-05-06T00:00:00Z","timestamp":1083801600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematische Nachrichten"],"published-print":{"date-parts":[[2004,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A two\u2010dimensional Reynolds type equation is derived and justified for a three\u2010dimensional viscous incompressible flow, taking place between two smooth fixed adjacent curved walls, under intensive percolation. Resulting from the dimension reduction, the model is proved to admit fluxes of order 1 = <jats:italic>h<\/jats:italic><jats:sup>0<\/jats:sup> with respect to the relative thickness <jats:italic>h<\/jats:italic>, a small parameter. Thus, velocities are allowed to be of order <jats:italic>h<\/jats:italic><jats:sup>\u22121<\/jats:sup>, which is just the case where linear and nonlinear terms have the same asymptotic powers <jats:italic>O<\/jats:italic>(<jats:italic>h<\/jats:italic><jats:sup>\u22123<\/jats:sup>). Boundary layers are also taken into account and estimates obtained for the remainder terms in the asymptotic representation formulae. (\u00a9 2004 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/mana.200310172","type":"journal-article","created":{"date-parts":[[2004,5,6]],"date-time":"2004-05-06T16:03:25Z","timestamp":1083859405000},"page":"189-209","source":"Crossref","is-referenced-by-count":6,"title":["Reynolds type equation for a thin flow under intensive transverse percolation"],"prefix":"10.1002","volume":"269-270","author":[{"given":"Sergue\u00ef","family":"Nazarov","sequence":"first","affiliation":[]},{"given":"Juha H.","family":"Videman","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2004,5,6]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1090\/qam\/693872","article-title":"Analysis of a free boundary problem in partial lubrication","volume":"40","author":"Bayada G.","year":"1982","journal-title":"Quart. Appl. Math."},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01442229"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1989230202051"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202599000609"},{"key":"e_1_2_1_6_2","first-page":"1115","article-title":"Loi d'\u00e9coulement non lin\u00e9aire entre deux plaques ondul\u00e9es","volume":"321","author":"Bourgeat A.","year":"1995","journal-title":"C. R. Acad. Sci. Paris, Ser. I Math."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202598000160"},{"key":"e_1_2_1_8_2","unstructured":"D.Gilbarg andN.Trudinger Elliptic Partial Differential Equations of Second Order 2nd ed. (Springer\u2010Verlag 1983)."},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827599360339"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.2000.3814"},{"key":"e_1_2_1_11_2","unstructured":"O.Ladyzhenskaya The Mathematical Theory of Viscous Incompressible Flow (Gordon and Breach New York 1969)."},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-001-0021-y"},{"key":"e_1_2_1_13_2","first-page":"59","article-title":"Asymptotic analysis of the Navier\u2010Stokes system in a plane domain with thin channels","volume":"23","author":"Maz'ya V. G.","year":"2000","journal-title":"Asymptot. Anal."},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1991250303631"},{"key":"e_1_2_1_15_2","first-page":"131","article-title":"Asymptotic solution of the Navier\u2010Stokes problem on the flow of a thin layer of fluid","volume":"31","author":"Nazarov S. A.","year":"1990","journal-title":"Sibirsk. Mat. Zh."},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1002\/1521-4001(200009)80:9<591::AID-ZAMM591>3.0.CO;2-Q"},{"key":"e_1_2_1_17_2","first-page":"95","article-title":"On the behavior of solutions of the Stokes and Navier\u2010Stokes systems in domains with a periodically varying section","volume":"159","author":"Nazarov S. A.","year":"1983","journal-title":"Trudy Mat. Inst. Steklov"},{"key":"e_1_2_1_18_2","first-page":"772","article-title":"Reynolds flow of a fluid in a thin three\u2010dimensional channel","volume":"30","author":"Nazarov S. A.","year":"1990","journal-title":"Litovsk. Mat. Sb."},{"key":"e_1_2_1_19_2","first-page":"141","article-title":"Asymptotic conditions at infinity for the Stokes and Navier\u2013Stokes problems in domains with cylindrical outlets to infinity","volume":"4","author":"Nazarov S. A.","year":"1999","journal-title":"Quaderni di Matematica"},{"key":"e_1_2_1_20_2","doi-asserted-by":"crossref","unstructured":"S. A.Nazarov andB. A.Plamenevskii Elliptic Problems in Domains with Piecewise Smooth Boundaries (Walter de Gruyter and Co Berlin 1994).","DOI":"10.1515\/9783110848915"},{"key":"e_1_2_1_21_2","doi-asserted-by":"publisher","DOI":"10.2206\/kyushujm.53.369"},{"key":"e_1_2_1_22_2","first-page":"137","article-title":"Estimates in Lp\n                   of solutions of elliptic and parabolic systems","volume":"102","author":"Solonnikov V. A.","year":"1967","journal-title":"Trudy MIAN"},{"key":"e_1_2_1_23_2","first-page":"147","article-title":"Stationary free boundary problems for the Navier\u2010Stokes equations","volume":"392","author":"Solonnikov V. A.","year":"1998","journal-title":"Advanced Topics in Theoretical Fluid Mechanics, Pitman Res. Notes Math."},{"key":"e_1_2_1_24_2","first-page":"135","article-title":"Probl\u00e8me de fronti\u00e9re libre dans l'ecoulement d'un liquide \u00e0 la sortie d'un tube cylindrique","volume":"17","author":"Solonnikov V. A.","year":"1998","journal-title":"Asymptot. Anal."}],"container-title":["Mathematische Nachrichten"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmana.200310172","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/mana.200310172","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T09:21:50Z","timestamp":1697620910000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/mana.200310172"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,5,6]]},"references-count":23,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2004,6]]}},"alternative-id":["10.1002\/mana.200310172"],"URL":"https:\/\/doi.org\/10.1002\/mana.200310172","archive":["Portico"],"relation":{},"ISSN":["0025-584X","1522-2616"],"issn-type":[{"value":"0025-584X","type":"print"},{"value":"1522-2616","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,5,6]]}}}