{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T06:54:54Z","timestamp":1648882494517},"reference-count":5,"publisher":"World Scientific Pub Co Pte Lt","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2005,11]]},"abstract":"<jats:p> We consider the [Formula: see text]-Navier\u2013Stokes System (NSS) on R<jats:sup>3<\/jats:sup> without external forcing. After Fourier transform we get a nonlocal nonlinear integral equation equivalent to NSS. For one-parameter families of initial conditions A \u00b7 c<jats:sup>(0)<\/jats:sup>(k)\/|k|<jats:sup>2<\/jats:sup> in the case of small |A| the NSS has a unique global solution. We argue that for large A NSS has no local solutions with these initial conditions. <\/jats:p>","DOI":"10.1142\/s0218127405014283","type":"journal-article","created":{"date-parts":[[2006,2,6]],"date-time":"2006-02-06T04:49:18Z","timestamp":1139201358000},"page":"3635-3637","source":"Crossref","is-referenced-by-count":0,"title":["ABSENCE OF THE LOCAL EXISTENCE THEOREM IN THE CRITICAL SPACE FOR THE $3\\mathcal{D}$-NAVIER\u2013STOKES SYSTEM"],"prefix":"10.1142","volume":"15","author":[{"given":"YAKOV","family":"SINAI","sequence":"first","affiliation":[{"name":"Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544-1000, USA"},{"name":"Landau Institute of Theoretical Physics, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","volume":"59","author":"Yu. Bakhtin Yu.","journal-title":"Russ. Math. Surv."},{"key":"rf3","first-page":"1","volume":"1","author":"Cannone M.","journal-title":"Rev. Math. Amer."},{"key":"rf4","volume-title":"Handbook of Math. Fluid Dynamics","volume":"3","author":"Cannone M.","year":"2002"},{"key":"rf5","first-page":"343","volume":"100","author":"Le Jan Y.","journal-title":"Prob. Th. Rel. Fields"},{"key":"rf6","volume-title":"Perspective in Analysis, Proc. Conf. Dedicated to the 75th Birthday of L. Carleson","author":"Sinai Ya. G.","year":"2005"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127405014283","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T11:03:35Z","timestamp":1565175815000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127405014283"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,11]]},"references-count":5,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2005,11]]}},"alternative-id":["10.1142\/S0218127405014283"],"URL":"https:\/\/doi.org\/10.1142\/s0218127405014283","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,11]]}}}