{"article_number":"77","status":"public","type":"journal_article","title":"Approximation of classical two-phase flows of viscous incompressible fluids by a Navier–Stokes/Allen–Cahn system","project":[{"grant_number":"948819","call_identifier":"H2020","name":"Bridging Scales in Random Materials","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d"}],"acknowledgement":"J. Fischer and M. Moser have received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 948819).\r\nOpen Access funding enabled and organized by Projekt DEAL.","date_updated":"2024-09-09T08:46:24Z","citation":{"ama":"Abels H, Fischer JL, Moser M. Approximation of classical two-phase flows of viscous incompressible fluids by a Navier–Stokes/Allen–Cahn system. <i>Archive for Rational Mechanics and Analysis</i>. 2024;248(5). doi:<a href=\"https://doi.org/10.1007/s00205-024-02020-9\">10.1007/s00205-024-02020-9</a>","chicago":"Abels, Helmut, Julian L Fischer, and Maximilian Moser. “Approximation of Classical Two-Phase Flows of Viscous Incompressible Fluids by a Navier–Stokes/Allen–Cahn System.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00205-024-02020-9\">https://doi.org/10.1007/s00205-024-02020-9</a>.","short":"H. Abels, J.L. Fischer, M. Moser, Archive for Rational Mechanics and Analysis 248 (2024).","ieee":"H. Abels, J. L. Fischer, and M. Moser, “Approximation of classical two-phase flows of viscous incompressible fluids by a Navier–Stokes/Allen–Cahn system,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 248, no. 5. Springer Nature, 2024.","ista":"Abels H, Fischer JL, Moser M. 2024. Approximation of classical two-phase flows of viscous incompressible fluids by a Navier–Stokes/Allen–Cahn system. Archive for Rational Mechanics and Analysis. 248(5), 77.","apa":"Abels, H., Fischer, J. L., &#38; Moser, M. (2024). Approximation of classical two-phase flows of viscous incompressible fluids by a Navier–Stokes/Allen–Cahn system. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-024-02020-9\">https://doi.org/10.1007/s00205-024-02020-9</a>","mla":"Abels, Helmut, et al. “Approximation of Classical Two-Phase Flows of Viscous Incompressible Fluids by a Navier–Stokes/Allen–Cahn System.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 248, no. 5, 77, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s00205-024-02020-9\">10.1007/s00205-024-02020-9</a>."},"publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"text":"We show convergence of the Navier-Stokes/Allen-Cahn system to a classical sharp interface model for the two-phase flow of two viscous incompressible fluids with same viscosities in a smooth bounded domain in two and three space dimensions as long as a smooth solution of the limit system exists. Moreover, we obtain error estimates with the aid of a relative entropy method. Our results hold provided that the mobility  mε>0  in the Allen-Cahn equation tends to zero in a subcritical way, i.e.,  mε=m0εβ  for some  β∈(0,2)  and  m0>0 . The proof proceeds by showing via a relative entropy argument that the solution to the Navier-Stokes/Allen-Cahn system remains close to the solution of a perturbed version of the two-phase flow problem, augmented by an extra mean curvature flow term  mεHΓt  in the interface motion. In a second step, it is easy to see that the solution to the perturbed problem is close to the original two-phase flow.","lang":"eng"}],"author":[{"full_name":"Abels, Helmut","last_name":"Abels","first_name":"Helmut"},{"orcid":"0000-0002-0479-558X","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","full_name":"Fischer, Julian L","last_name":"Fischer","first_name":"Julian L"},{"full_name":"Moser, Maximilian","id":"a60047a9-da77-11eb-85b4-c4dc385ebb8c","first_name":"Maximilian","last_name":"Moser"}],"external_id":{"arxiv":["2311.02997"]},"department":[{"_id":"JuFi"}],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"issue":"5","publisher":"Springer Nature","article_type":"original","publication_status":"published","_id":"17887","date_published":"2024-09-03T00:00:00Z","year":"2024","oa":1,"has_accepted_license":"1","date_created":"2024-09-08T22:01:10Z","quality_controlled":"1","day":"03","ec_funded":1,"language":[{"iso":"eng"}],"article_processing_charge":"Yes (via OA deal)","doi":"10.1007/s00205-024-02020-9","intvolume":"       248","ddc":["510"],"volume":248,"month":"09","scopus_import":"1","publication":"Archive for Rational Mechanics and Analysis","license":"https://creativecommons.org/licenses/by/4.0/","oa_version":"Published Version","file_date_updated":"2024-09-09T08:43:32Z","file":[{"file_id":"17938","creator":"dernst","success":1,"file_size":811131,"content_type":"application/pdf","access_level":"open_access","date_updated":"2024-09-09T08:43:32Z","file_name":"2024_ArchiveRatAnalysis_Abels.pdf","checksum":"98493a05b84e4513b6394dfad4851ddf","relation":"main_file","date_created":"2024-09-09T08:43:32Z"}]}