{"id":2056,"date":"2020-01-07T15:32:42","date_gmt":"2020-01-07T20:32:42","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/boyland\/?page_id=2056"},"modified":"2026-03-19T08:10:26","modified_gmt":"2026-03-19T12:10:26","slug":"alexis-vasseur","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/boyland\/alexis-vasseur\/","title":{"rendered":"Alexis Vasseur"},"content":{"rendered":"\r\n<section class=\"fullwidth-text-block\">\r\n\t<div class=\"container px-0 pt-5\">\r\n\t\t<div class=\"row align-items-start\">\r\n\t\t\t<div class=\"col-12\">\r\n\t\t\t\t\n<h1 class=\"wp-block-heading\">Alexis Vasseur<\/h1>\n\n\n\n<h3 class=\"wp-block-heading\">Paradoxes and challenges in the modeling of the viscosity for compressible viscous fluids<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"\">\u00a0Abstract:<\/span><\/p>\n\n\n\n<span class=\"\">The classical derivation of the viscosity coefficients, for a viscous fluids, usually predicts a dependence on the temperature of the fluids only. However, when considering \u00a0compressible fluids, this derivation leads to paradoxes associated to the possible presence of vacuum regions. When considering two disjoint bubbles of fluid, for instance, the associated compressible Navier-Stokes equation will predict unphysical \u00a0long range interactions between those two \u00a0bubbles. At the mathematical level, it implies the \u00a0non uniqueness of the solutions, and unphysical scenarios for blow-ups in finite time. One way to avoid these problems consists in adding a dependence of the viscosities with respect to the density of the fluid. This family of models can be rigorously justified in certain situations, as for the viscous shallow water equation for instance. These models display unexpected beautiful structures, but carry their own mathematical challenges, due to the degeneracy of the viscosities close to the vacuum.\u00a0We will discuss recent breakthroughs which have been accomplished recently to develop the mathematical grounding of these models (as, \u00a0for instance, Vasseur-Yu [Inventiones mathematicae (2016) and arXiv:1501.06803 (2015)] and \u00a0Li-Xin [arXiv:1504.06826 (2015)]).\u00a0<\/span>\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":146,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-2056","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/2056","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/users\/146"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/comments?post=2056"}],"version-history":[{"count":2,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/2056\/revisions"}],"predecessor-version":[{"id":3913,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/2056\/revisions\/3913"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/media?parent=2056"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}