{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T05:17:28Z","timestamp":1769836648385,"version":"3.49.0"},"reference-count":25,"publisher":"SAGE Publications","issue":"3-4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ASY"],"published-print":{"date-parts":[[2017,9,7]]},"DOI":"10.3233\/asy-171429","type":"journal-article","created":{"date-parts":[[2017,9,8]],"date-time":"2017-09-08T15:10:33Z","timestamp":1504883433000},"page":"167-190","source":"Crossref","is-referenced-by-count":6,"title":["Asymptotic expansion in Gevrey spaces for solutions of Navier\u2013Stokes equations"],"prefix":"10.1177","volume":"104","author":[{"given":"Luan T.","family":"Hoang","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Texas Tech University, Box 41042, Lubbock, TX 79409-1042, USA. E-mail:\u00a0luan.hoang@ttu.edu"}]},{"given":"Vincent R.","family":"Martinez","sequence":"additional","affiliation":[{"name":"Mathematics Department, Tulane University, 6823 St. Charles Ave, New Orleans, LA 70118, USA. E-mail:\u00a0vmartin6@tulane.edu"}]}],"member":"179","reference":[{"key":"10.3233\/ASY-171429_ref1","doi-asserted-by":"publisher","first-page":"2739","DOI":"10.1016\/j.jde.2012.08.003","article-title":"Gevrey regularity for a class of dissipative equations with applications to decay","volume":"253","author":"Biswas","year":"2012","journal-title":"J. Differential Equations"},{"issue":"3","key":"10.3233\/ASY-171429_ref2","doi-asserted-by":"publisher","first-page":"739","DOI":"10.1007\/s10231-012-0300-z","article-title":"On the maximal space analyticity radius for the 3D Navier\u2013Stokes equations and energy cascades","volume":"193","author":"Biswas","year":"2014","journal-title":"Ann. Mat. Pura Appl. (4)"},{"issue":"10","key":"10.3233\/ASY-171429_ref3","doi-asserted-by":"publisher","first-page":"3083","DOI":"10.1016\/j.jfa.2015.08.010","article-title":"On Gevrey regularity of the supercritical SQG equation in critical Besov spaces","volume":"269","author":"Biswas","year":"2015","journal-title":"J. Funct. Analysis"},{"key":"10.3233\/ASY-171429_ref4","doi-asserted-by":"crossref","unstructured":"P.\u00a0Constantin and C.\u00a0Foias, Navier\u2013Stokes Equations, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1988.","DOI":"10.7208\/chicago\/9780226764320.001.0001"},{"issue":"6","key":"10.3233\/ASY-171429_ref5","doi-asserted-by":"publisher","first-page":"1384","DOI":"10.1063\/1.868526","article-title":"Exponential decay rate of the power spectrum for solutions of the Naiver\u2013Stokes equations","volume":"7","author":"Doering","year":"1995","journal-title":"Phys. Fluids"},{"issue":"18","key":"10.3233\/ASY-171429_ref6","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1112\/plms\/s3-18.1.169","article-title":"Lower bounds for solutions of the Navier\u2013Stokes equations","volume":"3","author":"Dyer","year":"1968","journal-title":"Proc. London Math. Soc."},{"issue":"1","key":"10.3233\/ASY-171429_ref7","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1112\/plms\/pdl003","article-title":"On the helicity in 3D-periodic Navier\u2013Stokes equations. I. The non-statistical case","volume":"94","author":"Foias","year":"2007","journal-title":"Proc. Lond. Math. Soc. (3)"},{"issue":"2","key":"10.3233\/ASY-171429_ref8","doi-asserted-by":"publisher","first-page":"679","DOI":"10.1007\/s00220-009-0827-z","article-title":"On the helicity in 3D-periodic Navier\u2013Stokes equations. II. The statistical case","volume":"290","author":"Foias","year":"2009","journal-title":"Comm. Math. Phys."},{"issue":"2","key":"10.3233\/ASY-171429_ref9","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1512\/iumj.2006.55.2830","article-title":"On the solutions to the normal form of the Navier\u2013Stokes equations","volume":"55","author":"Foias","year":"2006","journal-title":"Indiana Univ. Math. J."},{"issue":"5","key":"10.3233\/ASY-171429_ref10","doi-asserted-by":"publisher","first-page":"1635","DOI":"10.1016\/j.anihpc.2008.09.003","article-title":"The normal form of the Navier\u2013Stokes equations in suitable normed spaces","volume":"26","author":"Foias","year":"2009","journal-title":"Ann. Inst. H. Poincar\u00e9 Anal. Non Lin\u00e9aire"},{"issue":"10","key":"10.3233\/ASY-171429_ref11","doi-asserted-by":"publisher","first-page":"3007","DOI":"10.1016\/j.jfa.2011.02.005","article-title":"Asymptotic integration of Navier\u2013Stokes equations with potential forces. II. An explicit Poincar\u00e9\u2013Dulac normal form","volume":"260","author":"Foias","year":"2011","journal-title":"J. Funct. Anal."},{"key":"10.3233\/ASY-171429_ref12","doi-asserted-by":"crossref","unstructured":"C.\u00a0Foias, O.\u00a0Manley, R.\u00a0Rosa and R.\u00a0Temam, Navier\u2013Stokes Equations and Turbulence, Encyclopedia of Mathematics and Its Applications, Vol.\u00a083, Cambridge University Press, Cambridge, 2001.","DOI":"10.1017\/CBO9780511546754"},{"issue":"3","key":"10.3233\/ASY-171429_ref13","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1512\/iumj.1984.33.33025","article-title":"Asymptotic behavior, as t \u2192 + \u221e, of solutions of Navier\u2013Stokes equations and nonlinear spectral manifolds","volume":"33","author":"Foias","year":"1984","journal-title":"Indiana Univ. Math. J."},{"issue":"1","key":"10.3233\/ASY-171429_ref14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0294-1449(16)30372-9","article-title":"Linearization and normal form of the Navier\u2013Stokes equations with potential forces","volume":"4","author":"Foias","year":"1987","journal-title":"Ann. Inst. H. Poincar\u00e9 Anal. Non Lin\u00e9aire"},{"issue":"1","key":"10.3233\/ASY-171429_ref15","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1512\/iumj.1991.40.40015","article-title":"Asymptotic integration of Navier\u2013Stokes equations with potential forces. I","volume":"40","author":"Foias","year":"1991","journal-title":"Indiana Univ. Math. J."},{"issue":"2","key":"10.3233\/ASY-171429_ref16","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1016\/0022-1236(89)90015-3","article-title":"Gevrey class regularity for the solutions of the Navier\u2013Stokes equations","volume":"87","author":"Foias","year":"1989","journal-title":"J. Funct. Anal."},{"key":"10.3233\/ASY-171429_ref17","doi-asserted-by":"crossref","unstructured":"U.\u00a0Frisch, Turbulence, Cambridge University Press, Cambridge, 1995, The legacy of A. N. Kolmogorov.","DOI":"10.1017\/CBO9781139170666"},{"issue":"1","key":"10.3233\/ASY-171429_ref18","doi-asserted-by":"publisher","first-page":"607","DOI":"10.1016\/j.jde.2010.08.016","article-title":"Asymptotic expansion for solutions of the Navier\u2013Stokes equations with potential forces","volume":"250","author":"Kukavica","year":"2011","journal-title":"J.\u00a0Differential Equations"},{"key":"10.3233\/ASY-171429_ref19","unstructured":"O.A.\u00a0Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach Science Publishers, New York, 1969, 2nd English edn, revised and enlarged. Translated from the Russian by R.A. Silverman and J.\u00a0Chu, Mathematics and Its Applications, Vol. 2."},{"key":"10.3233\/ASY-171429_ref20","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1006\/jdeq.1996.3200","article-title":"Analyticity of solutions for a generalized Euler equation","volume":"133","author":"Levermore","year":"1997","journal-title":"J. Differential Equations"},{"issue":"1","key":"10.3233\/ASY-171429_ref21","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1023\/A:1022696614020","article-title":"Investigation of the Foias\u2013Saut normalization in the finite-dimensional case","volume":"10","author":"Minea","year":"1998","journal-title":"J. Dynam. Differential Equations"},{"issue":"2","key":"10.3233\/ASY-171429_ref22","doi-asserted-by":"publisher","first-page":"292","DOI":"10.1006\/jdeq.1999.3744","article-title":"Gevrey regularity for the attractor of a partially dissipative model of B\u00e9nard convection in a porous medium","volume":"163","author":"Oliver","year":"2000","journal-title":"J. Differential Equations"},{"issue":"1","key":"10.3233\/ASY-171429_ref23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1006\/jfan.1999.3550","article-title":"Remark on the rate of decay of higher order derivatives for solutions to the Navier\u2013Stokes equations in R n","volume":"172","author":"Oliver","year":"2000","journal-title":"J. Funct. Anal."},{"issue":"1","key":"10.3233\/ASY-171429_ref24","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1006\/jdeq.2000.3927","article-title":"On the domain of analyticity of solutions of second order analytic nonlinear differential equations","volume":"174","author":"Oliver","year":"2001","journal-title":"J. Differential Equations"},{"key":"10.3233\/ASY-171429_ref25","doi-asserted-by":"crossref","unstructured":"R.\u00a0Temam, Navier\u2013Stokes Equations, AMS Chelsea Publishing, Providence, RI, 2001, Theory and numerical analysis, Reprint of the 1984 edition.","DOI":"10.1090\/chel\/343"}],"container-title":["Asymptotic Analysis"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/ASY-171429","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,11]],"date-time":"2025-03-11T08:47:43Z","timestamp":1741682863000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.medra.org\/servlet\/aliasResolver?alias=iospress&doi=10.3233\/ASY-171429"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,7]]},"references-count":25,"journal-issue":{"issue":"3-4"},"URL":"https:\/\/doi.org\/10.3233\/asy-171429","relation":{},"ISSN":["1875-8576","0921-7134"],"issn-type":[{"value":"1875-8576","type":"electronic"},{"value":"0921-7134","type":"print"}],"subject":[],"published":{"date-parts":[[2017,9,7]]}}}