{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T10:23:55Z","timestamp":1789727035465,"version":"4.0.1"},"reference-count":35,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","funder":[{"DOI":"10.13039\/501100005416","name":"Norwegian Research Council","doi-asserted-by":"crossref","award":["250302"],"award-info":[{"award-number":["250302"]}],"id":[{"id":"10.13039\/501100005416","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-161496"],"award-info":[{"award-number":["DMS-161496"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Math. Anal."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>This article establishes the global existence of weak solutions to a model proposed by Rosensweig [ Ferrohydrodynamics, Cambridge Monographs on Mechanics, Cambridge University Press, Cambridge, 1985] for the dynamics of ferrofluids. The system is expressed by the conservation of linear momentum, the incompressibility condition, the conservation of angular momentum, and the evolution of the magnetization. The existence proof is inspired by the DiPerna--Lions theory of renormalized solutions. In addition, the rigorous relaxation limit of the equations of ferrohydrodynamics towards the quasi-equilibrium is investigated. The proof relies on the relative entropy method, which involves constructing a suitable functional, analyzing its time evolution, and obtaining convergence results for the sequence of approximating solutions.<\/jats:p>","DOI":"10.1137\/18m1224957","type":"journal-article","created":{"date-parts":[[2019,11,5]],"date-time":"2019-11-05T12:18:20Z","timestamp":1572956300000},"page":"4245-4286","source":"Crossref","is-referenced-by-count":21,"title":["On the Dynamics of Ferrofluids: Global Weak Solutions to the Rosensweig System and Rigorous Convergence to Equilibrium"],"prefix":"10.1137","volume":"51","author":[{"given":"Ricardo H.","family":"Nochetto","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Konstantina","family":"Trivisa","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Franziska","family":"Weber","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,11,5]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2010.03.042"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/s00021-006-0234-6"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.70.460"},{"key":"atypb4","series-title":"Lecture Notes in Phys","first-page":"107","volume-title":"Nonlinear Problems in Theoretical Physics (Proceedings of the IX G.I.F.T. 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