{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:52:21Z","timestamp":1772297541840,"version":"3.50.1"},"reference-count":15,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2007,7,25]],"date-time":"2007-07-25T00:00:00Z","timestamp":1185321600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Commun. Math. Phys."],"published-print":{"date-parts":[[2007,8,8]]},"DOI":"10.1007\/s00220-007-0306-3","type":"journal-article","created":{"date-parts":[[2007,7,24]],"date-time":"2007-07-24T05:22:26Z","timestamp":1185254546000},"page":"255-269","source":"Crossref","is-referenced-by-count":48,"title":["Navier-Stokes Equation and Diffusions on the Group of Homeomorphisms of the Torus"],"prefix":"10.1007","volume":"275","author":[{"given":"F.","family":"Cipriano","sequence":"first","affiliation":[]},{"given":"A. B.","family":"Cruzeiro","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2007,7,25]]},"reference":[{"key":"306_CR1","doi-asserted-by":"crossref","first-page":"316","DOI":"10.5802\/aif.233","volume":"16","author":"V.I. Arnold","year":"1966","unstructured":"Arnold V.I. (1966). Sur la g\u00e9om\u00e9trie diff\u00e9rentielle des groupes de Lie de dimension infinie et ses applications a l\u2019hidrodynamique des fluides parfaits. Ann. Inst. Fourier 16: 316\u2013361","journal-title":"Ann. Inst. Fourier"},{"key":"306_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/b97593","volume-title":"Topological Methods in Hydrodynamics","author":"V.I. Arnold","year":"1998","unstructured":"Arnold V.I. and Khesin B.A. (1998). Topological Methods in Hydrodynamics. Springer-Verlag, New York"},{"issue":"3","key":"306_CR3","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1007\/s002200000349","volume":"216","author":"P. Constantin","year":"2001","unstructured":"Constantin P. (2001). An Eulerian-Lagrangian approach to the Navier-Stokes equations. Commun. Math. Phys. 216(3): 663\u2013686","journal-title":"Commun. Math. Phys."},{"key":"306_CR4","doi-asserted-by":"crossref","unstructured":"Constantin, P., Iyer, G.: A Stochastic Lagrangian Representation of 3-Dimensional Incompressible Navier-Stokes Equations. Comm. Pure Appl. Math., in press, DOI 10.1002\/cpa.20192, 2007","DOI":"10.1002\/cpa.20192"},{"key":"306_CR5","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1006\/jfan.2002.3922","volume":"196","author":"S. Fang","year":"2002","unstructured":"Fang S. (2002). Canonical Brownian motion on the diffeomorphism group of the circle. J. Funct. Anal. 196: 162\u2013179","journal-title":"J. Funct. Anal."},{"key":"306_CR6","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.jfa.2003.09.007","volume":"216","author":"S. Fang","year":"2004","unstructured":"Fang S. (2004). Solving s.d.e.\u2019s on Homeo S1. J. Funct. Anal. 216: 22\u201346","journal-title":"J. Funct. Anal."},{"key":"306_CR7","doi-asserted-by":"crossref","unstructured":"Gawedzki, K.: Simple models of turbulent transport. XIV Intern. Congress on Mathem. Physics, RiverEdge, NJ: World Scientific, 2005","DOI":"10.1142\/9789812704016_0005"},{"issue":"1","key":"306_CR8","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/s00220-004-1263-8","volume":"257","author":"D.A. Gomes","year":"2005","unstructured":"Gomes D.A. (2005). A variational formulation for the Navier-Stokes equation. Commun. Math. Phys. 257(1): 227\u2013234","journal-title":"Commun. Math. Phys."},{"key":"306_CR9","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1007\/BF01940961","volume":"65","author":"A. Inoue","year":"1979","unstructured":"Inoue A. and Funaki T. (1979). A new derivation of the Navier-Stokes equation. Commun. Math. Phys. 65: 83\u201390","journal-title":"Commun. Math. Phys."},{"key":"306_CR10","volume-title":"Stochastic Flows and Stochastic Differential Equations","author":"H. Kunita","year":"1990","unstructured":"Kunita H. (1990). Stochastic Flows and Stochastic Differential Equations. Cambridge University Press, Cambridge"},{"key":"306_CR11","doi-asserted-by":"crossref","unstructured":"Malliavin, P.: The canonic diffusion above the diffeomorphism group of the circle. C. R. Acad. Sci. Paris, t. 329, S\u00e9rie I, 325\u2013329 (1999)","DOI":"10.1016\/S0764-4442(00)88575-4"},{"key":"306_CR12","first-page":"337","volume":"160","author":"T. Nakagomi","year":"1981","unstructured":"Nakagomi T., Yasue K. and Zambrini J.C. (1981). Stochastic variational derivations of the Navier-Stokes equation. Lett. Math. Phys. 160: 337\u2013365","journal-title":"Lett. Math. Phys."},{"issue":"1","key":"306_CR13","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1006\/jfan.1998.3335","volume":"160","author":"S. Shkoller","year":"1998","unstructured":"Shkoller S. (1998). Geometry and curvature of diffeomorphism group with H1 metric and mean hydrodynamics. J. Funct. Anal. 160(1): 337\u2013365","journal-title":"J. Funct. Anal."},{"key":"306_CR14","doi-asserted-by":"crossref","unstructured":"\u00dcst\u00fcnel, A.S.: Stochastic analysis on Lie groups. Stoch. Anal. and Rel. Topics VI, Progr. Probab. 42, Boston: Birkh\u00e4user 1998","DOI":"10.1007\/978-1-4612-2022-0_3"},{"issue":"2","key":"306_CR15","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/0022-1236(83)90021-6","volume":"51","author":"K. Yasue","year":"1983","unstructured":"Yasue K. (1983). A variational principle for the Navier-Stokes equation. J. Funct. Anal. 51(2): 133\u2013141","journal-title":"J. Funct. Anal."}],"container-title":["Communications in Mathematical Physics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00220-007-0306-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00220-007-0306-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00220-007-0306-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,25]],"date-time":"2020-04-25T09:24:10Z","timestamp":1587806650000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00220-007-0306-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,7,25]]},"references-count":15,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2007,8,8]]}},"alternative-id":["306"],"URL":"https:\/\/doi.org\/10.1007\/s00220-007-0306-3","relation":{},"ISSN":["0010-3616","1432-0916"],"issn-type":[{"value":"0010-3616","type":"print"},{"value":"1432-0916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,7,25]]}}}