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Math. Anal."],"published-print":{"date-parts":[[2024,8,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We study statistical solutions of the incompressible Navier\u2013Stokes equation and their vanishing viscosity limit. We show that a formulation using correlation measures as in [U. S. Fjordholm, S. Lanthaler, and S. Mishra, Arch. Ration. Mech. Anal., 226 (2017), pp.\u00a0809\u2013849] and moment equations is equivalent to statistical solutions in the Foia\u015f\u2013Prodi sense. Under the assumption of weak scaling, a weaker version of Kolmogorov\u2019s self-similarity at small scales hypothesis that allows for intermittency corrections, we show that the limit is a statistical solution of the incompressible Euler equations. To pass to the limit, we derive a K\u00e1rm\u00e1n\u2013Howarth\u2013Monin relation for statistical solutions and combine it with the weak scaling assumption and a compactness theorem for correlation measures from [U. S. Fjordholm et al., Math. Models Methods Appl. Sci., 30 (2020), pp.\u00a0539\u2013609].<\/jats:p>","DOI":"10.1137\/23m1566261","type":"journal-article","created":{"date-parts":[[2024,7,15]],"date-time":"2024-07-15T04:01:51Z","timestamp":1721016111000},"page":"5099-5143","source":"Crossref","is-referenced-by-count":4,"title":["On the Vanishing Viscosity Limit of Statistical Solutions of the Incompressible Navier\u2013Stokes Equations"],"prefix":"10.1137","volume":"56","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8528-5786","authenticated-orcid":true,"given":"Ulrik Skre","family":"Fjordholm","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Oslo, Postboks 1053 Blindern, 0316 Oslo, Norway."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Siddhartha","family":"Mishra","sequence":"additional","affiliation":[{"name":"Seminar for Applied Mathematics (SAM), ETH Z\u00fcrich, HG G 57.2, R\u00e4mistrasse, 101, Z\u00fcrich, Switzerland."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Franziska","family":"Weber","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of California, Berkeley, Berkeley, CA 94720 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,7,15]]},"reference":[{"key":"ref1","volume-title":"Infinite Dimensional Analysis","author":"Aliprantis C. 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