{"acknowledgement":"We thank the anonymous referee for his/her careful reading of the manuscript and valuable suggestions. FC gratefully acknowledges funding from the Austrian Science Fund (FWF) through the project F65, and from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411.\r\nOpen access funding provided by Austrian Science Fund (FWF).","isi":1,"file_date_updated":"2024-01-30T12:09:34Z","ddc":["510"],"project":[{"name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","call_identifier":"H2020"},{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"intvolume":"       247","volume":247,"year":"2023","ec_funded":1,"article_type":"original","citation":{"short":"F. Cornalba, J.L. Fischer, Archive for Rational Mechanics and Analysis 247 (2023).","ama":"Cornalba F, Fischer JL. The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles. <i>Archive for Rational Mechanics and Analysis</i>. 2023;247(5). doi:<a href=\"https://doi.org/10.1007/s00205-023-01903-7\">10.1007/s00205-023-01903-7</a>","apa":"Cornalba, F., &#38; Fischer, J. L. (2023). The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-023-01903-7\">https://doi.org/10.1007/s00205-023-01903-7</a>","ista":"Cornalba F, Fischer JL. 2023. The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles. Archive for Rational Mechanics and Analysis. 247(5), 76.","chicago":"Cornalba, Federico, and Julian L Fischer. “The Dean-Kawasaki Equation and the Structure of Density Fluctuations in Systems of Diffusing Particles.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00205-023-01903-7\">https://doi.org/10.1007/s00205-023-01903-7</a>.","ieee":"F. Cornalba and J. L. Fischer, “The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 247, no. 5. Springer Nature, 2023.","mla":"Cornalba, Federico, and Julian L. Fischer. “The Dean-Kawasaki Equation and the Structure of Density Fluctuations in Systems of Diffusing Particles.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 247, no. 5, 76, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00205-023-01903-7\">10.1007/s00205-023-01903-7</a>."},"language":[{"iso":"eng"}],"article_number":"76","_id":"10551","doi":"10.1007/s00205-023-01903-7","has_accepted_license":"1","publication":"Archive for Rational Mechanics and Analysis","author":[{"full_name":"Cornalba, Federico","id":"2CEB641C-A400-11E9-A717-D712E6697425","last_name":"Cornalba","first_name":"Federico","orcid":"0000-0002-6269-5149"},{"orcid":"0000-0002-0479-558X","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","full_name":"Fischer, Julian L","last_name":"Fischer","first_name":"Julian L"}],"external_id":{"arxiv":["2109.06500"],"isi":["001043086800001"]},"publication_identifier":{"eissn":["1432-0673"],"issn":["0003-9527"]},"title":"The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles","quality_controlled":"1","status":"public","oa":1,"oa_version":"Published Version","date_created":"2021-12-16T12:16:03Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","scopus_import":"1","publication_status":"published","date_published":"2023-08-04T00:00:00Z","issue":"5","department":[{"_id":"JuFi"}],"abstract":[{"lang":"eng","text":"The Dean–Kawasaki equation—a strongly singular SPDE—is a basic equation of fluctuating hydrodynamics; it has been proposed in the physics literature to describe the fluctuations of the density of N independent diffusing particles in the regime of large particle numbers N≫1. The singular nature of the Dean–Kawasaki equation presents a substantial challenge for both its analysis and its rigorous mathematical justification. Besides being non-renormalisable by the theory of regularity structures by Hairer et al., it has recently been shown to not even admit nontrivial martingale solutions. In the present work, we give a rigorous and fully quantitative justification of the Dean–Kawasaki equation by considering the natural regularisation provided by standard numerical discretisations: We show that structure-preserving discretisations of the Dean–Kawasaki equation may approximate the density fluctuations of N non-interacting diffusing particles to arbitrary order in N−1  (in suitable weak metrics). In other words, the Dean–Kawasaki equation may be interpreted as a “recipe” for accurate and efficient numerical simulations of the density fluctuations of independent diffusing particles."}],"file":[{"date_created":"2024-01-30T12:09:34Z","file_size":1851185,"file_id":"14904","success":1,"date_updated":"2024-01-30T12:09:34Z","file_name":"2023_ArchiveRationalMech_Cornalba.pdf","creator":"dernst","access_level":"open_access","content_type":"application/pdf","relation":"main_file","checksum":"4529eeff170b6745a461d397ee611b5a"}],"type":"journal_article","license":"https://creativecommons.org/licenses/by/4.0/","day":"04","article_processing_charge":"Yes (via OA deal)","month":"08","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_updated":"2024-01-30T12:10:10Z"}