{"year":"2024","title":"Sharp interface limit for a Navier–Stokes/Allen–Cahn system in the case of a vanishing mobility","abstract":[{"text":"We consider the sharp interface limit of a Navier-Stokes/Allen Cahn equation in a bounded smooth domain in two space dimensions, in the case of vanishing mobility mε=ε√, where the small parameter ε>0 related to the thickness of the diffuse interface is sent to zero. For well-prepared initial data and sufficiently small times, we rigorously prove convergence to the classical two-phase Navier-Stokes system with surface tension. The idea of the proof is to use asymptotic expansions to construct an approximate solution and to estimate the difference of the exact and approximate solutions with a spectral estimate for the (at the approximate solution) linearized Allen-Cahn operator. In the calculations we use a fractional order ansatz and new ansatz terms in higher orders leading to a suitable ε-scaled and coupled model problem. Moreover, we apply the novel idea of introducing ε-dependent coordinates.","lang":"eng"}],"author":[{"first_name":"Helmut","full_name":"Abels, Helmut","last_name":"Abels"},{"last_name":"Fei","full_name":"Fei, Mingwen","first_name":"Mingwen"},{"last_name":"Moser","first_name":"Maximilian","id":"a60047a9-da77-11eb-85b4-c4dc385ebb8c","full_name":"Moser, Maximilian"}],"_id":"15334","date_updated":"2024-04-23T07:32:10Z","publication":"Calculus of Variations and Partial Differential Equations","article_type":"original","month":"05","intvolume":"        63","project":[{"grant_number":"948819","name":"Bridging Scales in Random Materials","call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d"}],"date_created":"2024-04-21T22:00:52Z","publication_status":"published","quality_controlled":"1","article_processing_charge":"Yes (via OA deal)","issue":"4","doi":"10.1007/s00526-024-02715-7","publisher":"Springer Nature","scopus_import":"1","day":"01","ec_funded":1,"citation":{"ieee":"H. Abels, M. Fei, and M. Moser, “Sharp interface limit for a Navier–Stokes/Allen–Cahn system in the case of a vanishing mobility,” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 63, no. 4. Springer Nature, 2024.","short":"H. Abels, M. Fei, M. Moser, Calculus of Variations and Partial Differential Equations 63 (2024).","chicago":"Abels, Helmut, Mingwen Fei, and Maximilian Moser. “Sharp Interface Limit for a Navier–Stokes/Allen–Cahn System in the Case of a Vanishing Mobility.” <i>Calculus of Variations and Partial Differential Equations</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00526-024-02715-7\">https://doi.org/10.1007/s00526-024-02715-7</a>.","apa":"Abels, H., Fei, M., &#38; Moser, M. (2024). Sharp interface limit for a Navier–Stokes/Allen–Cahn system in the case of a vanishing mobility. <i>Calculus of Variations and Partial Differential Equations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00526-024-02715-7\">https://doi.org/10.1007/s00526-024-02715-7</a>","ama":"Abels H, Fei M, Moser M. Sharp interface limit for a Navier–Stokes/Allen–Cahn system in the case of a vanishing mobility. <i>Calculus of Variations and Partial Differential Equations</i>. 2024;63(4). doi:<a href=\"https://doi.org/10.1007/s00526-024-02715-7\">10.1007/s00526-024-02715-7</a>","mla":"Abels, Helmut, et al. “Sharp Interface Limit for a Navier–Stokes/Allen–Cahn System in the Case of a Vanishing Mobility.” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 63, no. 4, 94, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s00526-024-02715-7\">10.1007/s00526-024-02715-7</a>.","ista":"Abels H, Fei M, Moser M. 2024. Sharp interface limit for a Navier–Stokes/Allen–Cahn system in the case of a vanishing mobility. Calculus of Variations and Partial Differential Equations. 63(4), 94."},"type":"journal_article","volume":63,"ddc":["510"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"file":[{"success":1,"file_name":"2024_CalculusEquations_Abels.pdf","content_type":"application/pdf","file_id":"15343","date_created":"2024-04-23T07:30:48Z","date_updated":"2024-04-23T07:30:48Z","relation":"main_file","file_size":975186,"access_level":"open_access","checksum":"b1095fad4cae596f52cc616a973bdde2","creator":"dernst"}],"publication_identifier":{"issn":["0944-2669"],"eissn":["1432-0835"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"acknowledgement":"Open Access funding enabled and organized by Projekt DEAL.\r\nM. Fei was partially supported by NSF of China under Grant No. 12271004 and Anhui Provincial Funding Project under Grant Nos. gxbjZD2022009 and 2308085J10. Moreover, M. Moser has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No 948819).","department":[{"_id":"JuFi"}],"language":[{"iso":"eng"}],"status":"public","article_number":"94","oa_version":"Published Version","has_accepted_license":"1","external_id":{"arxiv":["2304.12096"]},"file_date_updated":"2024-04-23T07:30:48Z","date_published":"2024-05-01T00:00:00Z"}