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We apply recently proved well-posedness and regularity results in order to establish existence of optimal controls as well as first-order necessary optimality conditions for an associated optimal control problem in which a distributed control is applied to the fluid flow.<\/jats:p>","DOI":"10.1137\/140994800","type":"journal-article","created":{"date-parts":[[2016,2,4]],"date-time":"2016-02-04T11:51:31Z","timestamp":1454586691000},"page":"221-250","source":"Crossref","is-referenced-by-count":59,"title":["Optimal Distributed Control of a Nonlocal Cahn--Hilliard\/Navier--Stokes System in Two Dimensions"],"prefix":"10.1137","volume":"54","author":[{"given":"Sergio","family":"Frigeri","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Elisabetta","family":"Rocca","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J\u00fcrgen","family":"Sprekels","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2016,2,4]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-008-0160-2"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.4064\/bc86-0-1"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2013.07.001"},{"key":"atypb4","unstructured":"S. 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Grasselli,\n                      On nonlocal Cahn-Hilliard-Navier-Stokes systems in two dimensions\n                      , preprint arXiv :1401.7954, 2014."},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1007\/s10884-012-9272-3"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.4310\/DPDE.2012.v9.n4.a1"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2013.07.016"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/28\/5\/1257"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1016\/j.anihpc.2009.11.013"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1007\/s11401-010-0603-6"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2010.11.014"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-247X(02)00425-0"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1007\/BF02181479"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139996313046"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/13\/6\/314"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.4171\/IFB\/270"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202596000341"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1007\/s00033-011-0139-y"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1137\/120865628"},{"key":"atypb31","unstructured":"M. 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