{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T11:03:40Z","timestamp":1774263820541,"version":"3.50.1"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2017,12,12]],"date-time":"2017-12-12T00:00:00Z","timestamp":1513036800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2017,12,12]],"date-time":"2017-12-12T00:00:00Z","timestamp":1513036800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N00014-15-1-2036"],"award-info":[{"award-number":["N00014-15-1-2036"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Nonlinear Sci"],"published-print":{"date-parts":[[2018,6]]},"DOI":"10.1007\/s00332-017-9429-7","type":"journal-article","created":{"date-parts":[[2017,12,12]],"date-time":"2017-12-12T12:33:47Z","timestamp":1513082027000},"page":"833-845","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Gas Near a Wall: Shortened Mean Free Path, Reduced Viscosity, and the Manifestation of the Knudsen Layer in the Navier\u2013Stokes Solution of a Shear Flow"],"prefix":"10.1007","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8309-1432","authenticated-orcid":false,"given":"Rafail V.","family":"Abramov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,12,12]]},"reference":[{"key":"9429_CR1","doi-asserted-by":"publisher","first-page":"532","DOI":"10.1016\/j.physa.2017.04.149","volume":"484","author":"RV Abramov","year":"2017","unstructured":"Abramov, R.V.: Diffusive Boltzmann equation, its fluid dynamics, Couette flow and Knudsen layers. Physica A 484, 532\u2013557 (2017)","journal-title":"Physica A"},{"key":"9429_CR2","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198561958.001.0001","volume-title":"Molecular Gas Dynamics and the Direct Simulation of Gas Flows","author":"GA Bird","year":"1994","unstructured":"Bird, G.A.: Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon, Oxford (1994)"},{"issue":"1","key":"9429_CR3","first-page":"1","volume":"I","author":"J Boussinesq","year":"1877","unstructured":"Boussinesq, J.: Essai sur la th\u00e9orie des eaux courantes. M\u00e9moires pr\u00e9sent\u00e9s par divers savants \u00e0 l\u2019Acad\u00e9mie des Sciences, XXII I(1), 1\u2013680 (1877)","journal-title":"M\u00e9moires pr\u00e9sent\u00e9s par divers savants \u00e0 l\u2019Acad\u00e9mie des Sciences, XXII"},{"key":"9429_CR4","volume-title":"The Mathematical Theory of Non-uniform Gases","author":"S Chapman","year":"1991","unstructured":"Chapman, S., Cowling, T.G.: The Mathematical Theory of Non-uniform Gases, 3rd edn. Cambridge Mathematical Library. Cambridge University Press, Cambridge (1991)","edition":"3"},{"key":"9429_CR5","doi-asserted-by":"publisher","first-page":"125502","DOI":"10.1088\/0022-3727\/44\/12\/125502","volume":"44","author":"N Dongari","year":"2011","unstructured":"Dongari, N., Zhang, Y., Reese, J.M.: Molecular free path distribution in rarefied gases. J. Phys. D Appl. Phys. 44, 125502 (2011)","journal-title":"J. Phys. D Appl. Phys."},{"issue":"3","key":"9429_CR6","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1111\/j.1745-6584.2003.tb02608.x","volume":"41","author":"PH Giao","year":"2003","unstructured":"Giao, P.H.: Revisit of well function approximation and an easy graphical curve matching technique for Theis\u2019 solution. Ground Water 41(3), 387\u2013390 (2003)","journal-title":"Ground Water"},{"key":"9429_CR7","volume-title":"Introduction to the Theory of Random Processes, Dover Books on Mathematics","author":"II Gikhman","year":"1996","unstructured":"Gikhman, I.I., Skorokhod, A.V.: Introduction to the Theory of Random Processes, Dover Books on Mathematics, 1969th edn. Dover Publications Inc., New York (1996)","edition":"1969"},{"issue":"4","key":"9429_CR8","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1002\/cpa.3160020403","volume":"2","author":"H Grad","year":"1949","unstructured":"Grad, H.: On the kinetic theory of rarefied gases. Commun. Pure Appl. Math. 2(4), 331\u2013407 (1949)","journal-title":"Commun. Pure Appl. Math."},{"key":"9429_CR9","doi-asserted-by":"publisher","first-page":"24001","DOI":"10.1209\/0295-5075\/80\/24001","volume":"80","author":"ZL Guo","year":"2007","unstructured":"Guo, Z.L., Shi, B.C., Zheng, C.G.: An extended Navier-Stokes formulation for gas flows in the Knudsen layer near a wall. Europhys. Lett. 80, 24001 (2007)","journal-title":"Europhys. Lett."},{"key":"9429_CR10","volume-title":"The Molecular Theory of Gases and Liquids","author":"JO Hirschfelder","year":"1964","unstructured":"Hirschfelder, J.O., Curtiss, C.F., Bird, R.B.: The Molecular Theory of Gases and Liquids. Wiley, New York (1964)"},{"key":"9429_CR11","doi-asserted-by":"publisher","first-page":"026315","DOI":"10.1103\/PhysRevE.76.026315","volume":"76","author":"CR Lilley","year":"2007","unstructured":"Lilley, C.R., Sader, J.E.: Velocity gradient singularity and structure of the velocity profile in the Knudsen layer according to the Boltzmann equation. Phys. Rev. E 76, 026315 (2007)","journal-title":"Phys. Rev. E"},{"key":"9429_CR12","doi-asserted-by":"publisher","first-page":"2015","DOI":"10.1098\/rspa.2008.0071","volume":"464","author":"CR Lilley","year":"2008","unstructured":"Lilley, C.R., Sader, J.E.: Velocity profile in the Knudsen layer according to the Boltzmann equation. Proc. R. Soc. A 464, 2015\u20132035 (2008)","journal-title":"Proc. R. Soc. A"},{"key":"9429_CR13","unstructured":"Mallinger, F.: Generalization of the Grad theory to polyatomic gases. Research Report 3581, Institut National de Recherche en Informatique et en Automatique (1998). E-print: INRIA-00073100"},{"issue":"10","key":"9429_CR14","doi-asserted-by":"publisher","first-page":"2107","DOI":"10.1063\/1.4824634","volume":"3","author":"SK Prabha","year":"2013","unstructured":"Prabha, S.K., Sreehari, P.D., Muraleedharan, M.G., Sathian, S.P.: The effect of system boundaries on the mean free path for confined gases. AIP Adv. 3(10), 2107 (2013)","journal-title":"AIP Adv."},{"issue":"10","key":"9429_CR15","doi-asserted-by":"publisher","first-page":"2078","DOI":"10.1016\/j.compfluid.2010.07.014","volume":"39","author":"TJ Scanlon","year":"2010","unstructured":"Scanlon, T.J., Roohi, E., White, C., Darbandi, M., Reese, J.M.: An open source, parallel DSMC code for rarefied gas flows in arbitrary geometries. Comput. Fluids 39(10), 2078\u20132089 (2010)","journal-title":"Comput. Fluids"},{"key":"9429_CR16","volume-title":"Kinetic Theory and Fluid Dynamics. Modeling and Simulation in Science, Engineering and Technology","author":"Y Sone","year":"2002","unstructured":"Sone, Y.: Kinetic Theory and Fluid Dynamics. Modeling and Simulation in Science, Engineering and Technology. Birkh\u00e4user, Basel (2002)"},{"key":"9429_CR17","doi-asserted-by":"publisher","first-page":"685","DOI":"10.1088\/0022-3727\/3\/5\/307","volume":"3","author":"DW Stops","year":"1970","unstructured":"Stops, D.W.: The mean free path of gas molecules in the transition regime. J. Phys. D Appl. Phys. 3, 685\u2013696 (1970)","journal-title":"J. Phys. D Appl. Phys."},{"key":"9429_CR18","volume-title":"Turbulence Modeling for CFD","author":"DC Wilcox","year":"1998","unstructured":"Wilcox, D.C.: Turbulence Modeling for CFD, 2nd edn. DCW Industries Inc., La Ca\u00f1ada, California (1998)","edition":"2"},{"key":"9429_CR19","doi-asserted-by":"publisher","first-page":"845","DOI":"10.1007\/s10404-012-1012-9","volume":"13","author":"W-M Zhang","year":"2012","unstructured":"Zhang, W.-M., Meng, G., Wei, X.: A review on slip models for gas microflows. Microfluid. Nanofluidics 13, 845\u2013882 (2012)","journal-title":"Microfluid. Nanofluidics"}],"container-title":["Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00332-017-9429-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-017-9429-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-017-9429-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,29]],"date-time":"2024-06-29T17:02:39Z","timestamp":1719680559000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00332-017-9429-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12,12]]},"references-count":19,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,6]]}},"alternative-id":["9429"],"URL":"https:\/\/doi.org\/10.1007\/s00332-017-9429-7","relation":{},"ISSN":["0938-8974","1432-1467"],"issn-type":[{"value":"0938-8974","type":"print"},{"value":"1432-1467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,12,12]]},"assertion":[{"value":"30 May 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 December 2017","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 December 2017","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}