{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:48:46Z","timestamp":1777448926799,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2012,3,1]],"date-time":"2012-03-01T00:00:00Z","timestamp":1330560000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2012,3]]},"abstract":"<jats:p>We construct the weakly nonlinear-dissipative approximate system for the general compressible Navier\u2013Stokes system in a periodic domain. It was shown in Arch. Rational Mech. Anal. 201 (2011), 377\u2013412, that because the Navier\u2013Stokes system has an entropy structure, its approximate system will have Leray-like global weak solutions. These solutions decompose into an incompressible part governed by an incompressible Navier\u2013Stokes system, and an acoustic part governed by a nonlocal quadratic equation which couples it to the incompressible part. We obtain regularity results for the acoustic part of the solution via a Littlewood\u2013Paley decomposition that extend to this general setting results found by Masmoudi [Ann. Inst. H. Poincar\u00e9 18 (2001), 199\u2013224] and Danchin [Amer. J. Math. 124 (2002), 1153\u20131219] in the \u03b3-law barotropic setting.<\/jats:p>","DOI":"10.3233\/asy-2011-1066","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:19:40Z","timestamp":1575055180000},"page":"61-86","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["Global existence and regularity of the weakly compressible Navier\u2013Stokes system"],"prefix":"10.1177","volume":"76","author":[{"given":"Ning","family":"Jiang","sequence":"first","affiliation":[{"name":"Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA. E-mail: njiang@math.tsinghua.edu.cn"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"C. David","family":"Levermore","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA. E-mail: lvrmr@math.umd.edu"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2012,3,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2011-1066","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2011-1066","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:39:26Z","timestamp":1777379966000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-2011-1066"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2012,3]]}},"alternative-id":["10.3233\/ASY-2011-1066"],"URL":"https:\/\/doi.org\/10.3233\/asy-2011-1066","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,3]]}}}