{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:21:58Z","timestamp":1787329318870,"version":"build-2736575974"},"reference-count":12,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>In their 2006 paper, Chernyshenko et al. [J. Math. Phys., 48 (2007), 065204, 15 pp]. prove that a sufficiently smooth strong solution of the 3D Navier\u2013Stokes equations is robust with respect to small enough changes in initial conditions and forcing function. They also show that if a regular enough strong solution exists, then Galerkin approximations converge to it. They then use these results to conclude that the existence of a sufficiently regular strong solution can be verified using sufficiently refined numerical computations. In this paper we study the strong solutions with less regularity than those considered in Chernyshenko et al. [J. Math. Phys., 48 (2007), 065204, 15 pp]. We prove a similar robustness result and show the validity of the results relating convergent numerical computations and the existence of the strong solutions.<\/jats:p>","DOI":"10.1137\/060677537","type":"journal-article","created":{"date-parts":[[2008,9,4]],"date-time":"2008-09-04T19:18:32Z","timestamp":1220555912000},"page":"3136-3150","source":"Crossref","is-referenced-by-count":10,"title":["An A Posteriori Condition on the Numerical Approximations of the Navier\u2013Stokes Equations for the Existence of a Strong Solution"],"prefix":"10.1137","volume":"46","author":[{"given":"Masoumeh","family":"Dashti","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"James C.","family":"Robinson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,9,4]]},"reference":[{"key":"R1","unstructured":"R. A. Adams,\n                      Sobolev Spaces\n                      , Academic Press, New York, 1975."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1063\/1.2372512"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"P. Constantin and C. Foias,\n                      Navier\u2013Stokes Equations\n                      , University of Chicago Press, Chicago, 1988.","DOI":"10.7208\/chicago\/9780226764320.001.0001"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1993-1160273-1"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/0730032"},{"key":"R6","first-page":"889","volume":"21","author":"Fursikov A. V.","year":"1980","journal-title":"Soviet Math. Dokl.","ISSN":"https:\/\/id.crossref.org\/issn\/0197-6788","issn-type":"print"},{"key":"R7","unstructured":"D. Gilbarg and N.S. Trudinger,\n                      Elliptic partial differential equations of second order\n                      , Springer-Verlag, Berlin, 1983."},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/0719018"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(72)90003-1"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/BF00252910"},{"key":"R11","unstructured":"J. C. Robinson,\n                      Infinite-dimensional Dynamical Systems\n                      , Cambridge University Press, Cambridge, 2001."},{"key":"R12","unstructured":"R. Temam,\n                      Navier\u2013Stokes Equations and Nonlinear Functional Analysis\n                      , SIAM, Philadelphia, 1983."}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/060677537","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:14:57Z","timestamp":1787325297000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/060677537"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":12,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/060677537"],"URL":"https:\/\/doi.org\/10.1137\/060677537","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1]]}}}