{"date_updated":"2023-09-19T10:39:09Z","month":"08","department":[{"_id":"JuFi"}],"title":"Well-posedness for mean-field evolutions arising in superconductivity","day":"01","language":[{"iso":"eng"}],"year":"2018","acknowledgement":"The work of the author is supported by F.R.S.-FNRS ( Fonds de la Recherche Scientifique - FNRS ) through a Research Fellowship.\r\n\r\n","publication":"Annales de l'Institut Henri Poincare (C) Non Linear Analysis","abstract":[{"lang":"eng","text":"We establish the existence of a global solution for a new family of fluid-like equations, which are obtained in certain regimes in as the mean-field evolution of the supercurrent density in a (2D section of a) type-II superconductor with pinning and with imposed electric current. We also consider general vortex-sheet initial data, and investigate the uniqueness and regularity properties of the solution. For some choice of parameters, the equation under investigation coincides with the so-called lake equation from 2D shallow water fluid dynamics, and our analysis then leads to a new existence result for rough initial data."}],"article_processing_charge":"No","scopus_import":"1","author":[{"last_name":"Duerinckx","first_name":"Mitia","full_name":"Duerinckx, Mitia"},{"id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","last_name":"Fischer","first_name":"Julian L","full_name":"Fischer, Julian L","orcid":"0000-0002-0479-558X"}],"oa":1,"external_id":{"arxiv":["1607.00268"],"isi":["000437975500005"]},"volume":35,"publication_status":"published","publisher":"Elsevier","doi":"10.1016/j.anihpc.2017.11.004","date_created":"2018-12-11T11:47:27Z","main_file_link":[{"url":"https://arxiv.org/abs/1607.00268","open_access":"1"}],"citation":{"ieee":"M. Duerinckx and J. L. Fischer, “Well-posedness for mean-field evolutions arising in superconductivity,” <i>Annales de l’Institut Henri Poincare (C) Non Linear Analysis</i>, vol. 35, no. 5. Elsevier, pp. 1267–1319, 2018.","chicago":"Duerinckx, Mitia, and Julian L Fischer. “Well-Posedness for Mean-Field Evolutions Arising in Superconductivity.” <i>Annales de l’Institut Henri Poincare (C) Non Linear Analysis</i>. Elsevier, 2018. <a href=\"https://doi.org/10.1016/j.anihpc.2017.11.004\">https://doi.org/10.1016/j.anihpc.2017.11.004</a>.","ama":"Duerinckx M, Fischer JL. Well-posedness for mean-field evolutions arising in superconductivity. <i>Annales de l’Institut Henri Poincare (C) Non Linear Analysis</i>. 2018;35(5):1267-1319. doi:<a href=\"https://doi.org/10.1016/j.anihpc.2017.11.004\">10.1016/j.anihpc.2017.11.004</a>","mla":"Duerinckx, Mitia, and Julian L. Fischer. “Well-Posedness for Mean-Field Evolutions Arising in Superconductivity.” <i>Annales de l’Institut Henri Poincare (C) Non Linear Analysis</i>, vol. 35, no. 5, Elsevier, 2018, pp. 1267–319, doi:<a href=\"https://doi.org/10.1016/j.anihpc.2017.11.004\">10.1016/j.anihpc.2017.11.004</a>.","ista":"Duerinckx M, Fischer JL. 2018. Well-posedness for mean-field evolutions arising in superconductivity. Annales de l’Institut Henri Poincare (C) Non Linear Analysis. 35(5), 1267–1319.","apa":"Duerinckx, M., &#38; Fischer, J. L. (2018). Well-posedness for mean-field evolutions arising in superconductivity. <i>Annales de l’Institut Henri Poincare (C) Non Linear Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.anihpc.2017.11.004\">https://doi.org/10.1016/j.anihpc.2017.11.004</a>","short":"M. Duerinckx, J.L. Fischer, Annales de l’Institut Henri Poincare (C) Non Linear Analysis 35 (2018) 1267–1319."},"oa_version":"Submitted Version","_id":"606","issue":"5","publist_id":"7199","intvolume":"        35","date_published":"2018-08-01T00:00:00Z","page":"1267-1319","arxiv":1,"status":"public","quality_controlled":"1","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","isi":1,"type":"journal_article"}