{"day":"10","date_updated":"2023-08-18T10:26:07Z","issue":"2","external_id":{"isi":["000508175400001"],"arxiv":["1811.06448"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"01","abstract":[{"text":"The evolution of finitely many particles obeying Langevin dynamics is described by Dean–Kawasaki equations, a class of stochastic equations featuring a non-Lipschitz multiplicative noise in divergence form. We derive a regularised Dean–Kawasaki model based on second order Langevin dynamics by analysing a system of particles interacting via a pairwise potential. Key tools of our analysis are the propagation of chaos and Simon's compactness criterion. The model we obtain is a small-noise stochastic perturbation of the undamped McKean–Vlasov equation. We also provide a high-probability result for existence and uniqueness for our model.","lang":"eng"}],"language":[{"iso":"eng"}],"isi":1,"scopus_import":"1","citation":{"chicago":"Cornalba, Federico, Tony Shardlow, and Johannes Zimmer. “From Weakly Interacting Particles to a Regularised Dean-Kawasaki Model.” <i>Nonlinearity</i>. IOP Publishing, 2020. <a href=\"https://doi.org/10.1088/1361-6544/ab5174\">https://doi.org/10.1088/1361-6544/ab5174</a>.","short":"F. Cornalba, T. Shardlow, J. Zimmer, Nonlinearity 33 (2020) 864–891.","ama":"Cornalba F, Shardlow T, Zimmer J. From weakly interacting particles to a regularised Dean-Kawasaki model. <i>Nonlinearity</i>. 2020;33(2):864-891. doi:<a href=\"https://doi.org/10.1088/1361-6544/ab5174\">10.1088/1361-6544/ab5174</a>","ista":"Cornalba F, Shardlow T, Zimmer J. 2020. From weakly interacting particles to a regularised Dean-Kawasaki model. Nonlinearity. 33(2), 864–891.","ieee":"F. Cornalba, T. Shardlow, and J. Zimmer, “From weakly interacting particles to a regularised Dean-Kawasaki model,” <i>Nonlinearity</i>, vol. 33, no. 2. IOP Publishing, pp. 864–891, 2020.","apa":"Cornalba, F., Shardlow, T., &#38; Zimmer, J. (2020). From weakly interacting particles to a regularised Dean-Kawasaki model. <i>Nonlinearity</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/1361-6544/ab5174\">https://doi.org/10.1088/1361-6544/ab5174</a>","mla":"Cornalba, Federico, et al. “From Weakly Interacting Particles to a Regularised Dean-Kawasaki Model.” <i>Nonlinearity</i>, vol. 33, no. 2, IOP Publishing, 2020, pp. 864–91, doi:<a href=\"https://doi.org/10.1088/1361-6544/ab5174\">10.1088/1361-6544/ab5174</a>."},"date_published":"2020-01-10T00:00:00Z","oa":1,"year":"2020","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1811.06448"}],"_id":"7637","article_type":"original","publication_status":"published","intvolume":"        33","doi":"10.1088/1361-6544/ab5174","author":[{"full_name":"Cornalba, Federico","last_name":"Cornalba","first_name":"Federico","orcid":"0000-0002-6269-5149","id":"2CEB641C-A400-11E9-A717-D712E6697425"},{"first_name":"Tony","last_name":"Shardlow","full_name":"Shardlow, Tony"},{"first_name":"Johannes","full_name":"Zimmer, Johannes","last_name":"Zimmer"}],"type":"journal_article","publication_identifier":{"eissn":["13616544"],"issn":["09517715"]},"status":"public","department":[{"_id":"JuFi"}],"publisher":"IOP Publishing","article_processing_charge":"No","publication":"Nonlinearity","date_created":"2020-04-05T22:00:49Z","title":"From weakly interacting particles to a regularised Dean-Kawasaki model","page":"864-891","oa_version":"Preprint","quality_controlled":"1","volume":33}