{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T04:40:24Z","timestamp":1759984824783,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T00:00:00Z","timestamp":1759795200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Heilongjiang Province\u2019s Basic Research Support Program for Excellent Young Teachers","award":["YQJH2023086"],"award-info":[{"award-number":["YQJH2023086"]}]},{"name":"Northeast Petroleum University Talent Introduction and Research Initiation Funding Project","award":["2021KQ18"],"award-info":[{"award-number":["2021KQ18"]}]},{"name":"Northeast Petroleum University National Natural Science Foundation Cultivation Fund","award":["2023GPL-14"],"award-info":[{"award-number":["2023GPL-14"]}]},{"name":"Heilongjiang Outbound Postdoctoral Funding","award":["216240064"],"award-info":[{"award-number":["216240064"]}]},{"name":"Heilongjiang Postdoctoral Foundation","award":["LBH-Z22043","LBH-Z20101"],"award-info":[{"award-number":["LBH-Z22043","LBH-Z20101"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["52104065","51674086"],"award-info":[{"award-number":["52104065","51674086"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["www.mdpi.com"],"crossmark-restriction":true},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this study, we employ the homotopy renormalization (HTR) method to analytically investigate Rasmussen\u2019s problem, which characterizes the viscous fluid motion between a pair of infinitely large, coaxially rotating disks. The original set of nonlinear ordinary differential equations is reformulated within a homotopy-based framework, allowing us to construct global asymptotic approximations with closed-form expressions. The HTR method overcomes the limitations of traditional perturbation and renormalization techniques, and avoids the need for asymptotic matching. In addition, the analytic expressions allow for direct estimation of flow parameters such as boundary layer thickness. These results demonstrate the effectiveness of the HTR method in asymptotic analysis and highlight its potential for broader applications in nonlinear fluid dynamics.<\/jats:p>","DOI":"10.3390\/sym17101674","type":"journal-article","created":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T08:05:36Z","timestamp":1759824336000},"page":"1674","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Global Solutions to Rasmussen\u2019s Problem by Homotopy Renormalization Method"],"prefix":"10.3390","volume":"17","author":[{"given":"Bing","family":"Guan","sequence":"first","affiliation":[{"name":"State Key Laboratory of Continental Shale Oil, Northeast Petroleum University, Daqing 163318, China"},{"name":"Postdoctoral Programme of Daqing Oilfield, Daqing 163318, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xianjun","family":"Wang","sequence":"additional","affiliation":[{"name":"Daqing Oilfield Co., Ltd., Oil Production Technology Research Institute, Daqing 163318, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaofei","family":"Fu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Continental Shale Oil, Northeast Petroleum University, Daqing 163318, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1584-0315","authenticated-orcid":false,"given":"Shuangqing","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Petroleum Engineering, Northeast Petroleum University, Daqing 163318, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shibin","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Continental Shale Oil, Northeast Petroleum University, Daqing 163318, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,7]]},"reference":[{"key":"ref_1","first-page":"382","article-title":"Construction for Direct-Reading Scales for the Slide Wire Bridge","volume":"17","author":"Buckingham","year":"1903","journal-title":"Phys. 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