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Math. Anal."],"published-print":{"date-parts":[[2024,10,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this paper, we consider the one time-varying component regularity criteria for a local strong solution of 3-D Navier\u2013Stokes equations. Precisely, if [Formula: see text] is a piecewise [Formula: see text] unit vector from [Formula: see text] to [Formula: see text] with finitely many jump discontinuities, we prove that if [Formula: see text], then the solution [Formula: see text] can be extended beyond the time [Formula: see text]. Compared with the previous results J.-Y. Chemin and P. Zhang, Ann.\u00a0Sci.\u00a0\u00c9c.\u00a0Norm.\u00a0Sup\u00e9r, 4 (2016), pp.\u00a049\u2013167 concerning one-component regularity criteria, here the unit vector [Formula: see text] varies\u00a0with the time variable.<\/jats:p>","DOI":"10.1137\/23m1623124","type":"journal-article","created":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T04:02:25Z","timestamp":1725508945000},"page":"6213-6231","source":"Crossref","is-referenced-by-count":2,"title":["On the One Time-Varying Component Regularity Criteria for 3-D Navier-Stokes Equations"],"prefix":"10.1137","volume":"56","author":[{"given":"Yanlin","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, MOE, Beijing Normal University, 100875 Beijing, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ping","family":"Zhang","sequence":"additional","affiliation":[{"name":"Academy of Mathematics & Systems Science and Hua Loo-Keng Center for Mathematical Sciences, Chinese Academy of Sciences, Beijing 100190, China, and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,9,5]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-0939-9_5"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-16830-7"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.24033\/asens.1404"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.2008.57.3719"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-011-0439-6"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-021-01636-5"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-007-0236-0"},{"key":"ref8","first-page":"49","volume":"4","author":"Chemin J.-Y.","year":"2016","journal-title":"Ann. 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