{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T09:05:35Z","timestamp":1775120735842,"version":"3.50.1"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2009,10,10]],"date-time":"2009-10-10T00:00:00Z","timestamp":1255132800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Nonlinear Sci"],"published-print":{"date-parts":[[2010,2]]},"DOI":"10.1007\/s00332-009-9051-4","type":"journal-article","created":{"date-parts":[[2009,10,9]],"date-time":"2009-10-09T18:37:24Z","timestamp":1255113444000},"page":"81-103","source":"Crossref","is-referenced-by-count":6,"title":["Dissipative N-point-vortex Models in the Plane"],"prefix":"10.1007","volume":"20","author":[{"given":"Banavara N.","family":"Shashikanth","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2009,10,10]]},"reference":[{"key":"9051_CR1","series-title":"Applied Mathematical Sciences","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1029-0","volume-title":"Manifolds, Tensor Analysis, and Applications","author":"R. Abraham","year":"1988","unstructured":"Abraham, R., Marsden, J.E., Ratiu, T.: Manifolds, Tensor Analysis, and Applications, 2nd edn. Applied Mathematical Sciences, vol.\u00a075, Springer, New York (1988)","edition":"2"},{"issue":"12","key":"9051_CR2","doi-asserted-by":"crossref","first-page":"2361","DOI":"10.1103\/PhysRevLett.78.2361","volume":"78","author":"O. Agullo","year":"1997","unstructured":"Agullo, O., Verga, A.D.: Exact two vortices solution of Navier\u2013Stokes equations. Phys. Rev. Lett. 78(12), 2361\u20132364 (1997)","journal-title":"Phys. Rev. Lett."},{"key":"9051_CR3","doi-asserted-by":"crossref","first-page":"056304-1","DOI":"10.1103\/PhysRevE.63.056304","volume":"63","author":"O. Agullo","year":"2001","unstructured":"Agullo, O., Verga, A.D.: Effect of viscosity in the dynamics of two point vortices: exact results. Phys. Rev. E 63, 056304-1\u2013056304-14 (2001)","journal-title":"Phys. Rev. E"},{"key":"9051_CR4","unstructured":"Baleanu, D., Makhaldiani, N.: Nambu\u2013Poisson reformulation of the finite dimensional dynamical systems. arXiv:solv-int\/9903002v1 (1999)"},{"key":"9051_CR5","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/BF02099528","volume":"147","author":"A.M. Bloch","year":"1992","unstructured":"Bloch, A.M., Brockett, R.W., Ratiu, T.S.: Completely integrable gradient flows. Commun. Math. Phys. 147, 57\u201374 (1992)","journal-title":"Commun. Math. Phys."},{"key":"9051_CR6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02101622","volume":"175","author":"A.M. Bloch","year":"1996","unstructured":"Bloch, A.M., Krishnaprasad, P.S., Marsden, J.E., Ratiu, T.S.: The Euler\u2013Poincar\u00e9 equations and double bracket dissipation. Commun. Math. Phys. 175, 1\u201342 (1996)","journal-title":"Commun. Math. Phys."},{"key":"9051_CR7","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1007\/s002200050140","volume":"187","author":"A.M. Bloch","year":"1997","unstructured":"Bloch, A.M., Brockett, R.W., Crouch, P.: Double bracket equations and geodesic flows on symmetric spaces. Commun. Math. Phys. 187, 357\u2013373 (1997)","journal-title":"Commun. Math. Phys."},{"key":"9051_CR8","unstructured":"Boatto, S., Koiller, J.: Vortices on closed surfaces. arXiv:0802.4313 (2008)"},{"key":"9051_CR9","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/0024-3795(91)90021-N","volume":"146","author":"R.W. Brockett","year":"1991","unstructured":"Brockett, R.W.: Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems. Linear Algebra Appl. 146, 79\u201391 (1991)","journal-title":"Linear Algebra Appl."},{"issue":"I","key":"9051_CR10","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1090\/pspum\/054.1\/1216576","volume":"54","author":"R.W. Brockett","year":"1993","unstructured":"Brockett, R.W.: Differential geometry and the design of gradient algorithms. Proc. Symp. Pure Math., AMS 54(I), 69\u201392 (1993)","journal-title":"Proc. Symp. Pure Math., AMS"},{"key":"9051_CR11","first-page":"69","volume":"3","author":"R.W. Brockett","year":"1994","unstructured":"Brockett, R.W.: The double bracket equation as a solution of a variational problem. Fields Inst. Commun. 3, 69\u201376 (1994)","journal-title":"Fields Inst. Commun."},{"key":"9051_CR12","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1007\/BF00714375","volume":"36","author":"R. Chatterjee","year":"1996","unstructured":"Chatterjee, R.: Dynamical symmetries and Nambu mechanics. Lett. Math. Phys. 36, 117 (1996)","journal-title":"Lett. Math. Phys."},{"issue":"4","key":"9051_CR13","doi-asserted-by":"crossref","first-page":"785","DOI":"10.1017\/S0022112073002016","volume":"57","author":"A.J. Chorin","year":"1973","unstructured":"Chorin, A.J.: Numerical study of slightly viscous flow. J. Fluid Mech. 57(4), 785\u2013796 (1973)","journal-title":"J. Fluid Mech."},{"key":"9051_CR14","doi-asserted-by":"crossref","first-page":"428","DOI":"10.1016\/0021-9991(78)90019-0","volume":"27","author":"A.J. Chorin","year":"1978","unstructured":"Chorin, A.J.: Vortex sheet approximation of boundary layers. J.\u00a0Comput. Phys. 27, 428\u2013442 (1978)","journal-title":"J.\u00a0Comput. Phys."},{"key":"9051_CR15","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511526442","volume-title":"Vortex Methods: Theory and Practice","author":"G.-H. Cottet","year":"2000","unstructured":"Cottet, G.-H., Koumoutsakos, P.: Vortex Methods: Theory and Practice. Cambridge University Press, Cambridge (2000)"},{"key":"9051_CR16","series-title":"Universitext","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-57951-6","volume-title":"Differential Forms and Applications","author":"M.P. Carmo do","year":"1994","unstructured":"do Carmo, M.P.: Differential Forms and Applications. Universitext, Springer, Berlin (1994)"},{"issue":"3","key":"9051_CR17","doi-asserted-by":"crossref","first-page":"325","DOI":"10.2991\/jnmp.2001.8.3.2","volume":"8","author":"P. Guha","year":"2001","unstructured":"Guha, P.: Volume preserving multidimensional integrable systems and Nambu\u2013Poisson geometry. J. Nonlin. Math. Phys. 8(3), 325\u2013341 (2001)","journal-title":"J. Nonlin. Math. Phys."},{"issue":"2","key":"9051_CR18","doi-asserted-by":"crossref","first-page":"223","DOI":"10.2991\/jnmp.2004.11.2.7","volume":"11","author":"P. Guha","year":"2004","unstructured":"Guha, P.: Applications of Nambu Mechanics to Systems of Hydrodynamical Type II. J. Nonlin. Math. Phys. 11(2), 223\u2013232 (2004)","journal-title":"J. Nonlin. Math. Phys."},{"key":"9051_CR19","doi-asserted-by":"crossref","DOI":"10.1142\/p557","volume-title":"Geometric Mechanics, Part I: Dynamics and Symmetry","author":"D.D. Holm","year":"2008","unstructured":"Holm, D.D.: Geometric Mechanics, Part I: Dynamics and Symmetry. Imperial College Press, London (2008a)"},{"key":"9051_CR20","doi-asserted-by":"crossref","DOI":"10.1142\/p549","volume-title":"Geometric Mechanics, Part II: Rotating, Translating and Rolling","author":"D.D. Holm","year":"2008","unstructured":"Holm, D.D.: Geometric Mechanics, Part II: Rotating, Translating and Rolling. Imperial College Press, London (2008b)"},{"key":"9051_CR21","author":"D.D. Holm","year":"2008","unstructured":"Holm, D.D., Putkaradze, V., Tronci, C.: Geometric gradient-flow dynamics with singular solutions. Physica D (2008). doi: 10.1016\/j.physd.2008.04.010","journal-title":"Physica D"},{"key":"9051_CR22","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/S0167-2789(97)00236-4","volume":"116","author":"R. Kidambi","year":"1998","unstructured":"Kidambi, R., Newton, P.K.: Motion of three point vortices on a sphere. Physica D 116, 143\u2013175 (1998)","journal-title":"Physica D"},{"key":"9051_CR23","series-title":"Encyclopedia of Mathematical Sciences","volume-title":"Dynamical Systems X: General Theory of Vortices","author":"V.V. Kozlov","year":"2008","unstructured":"Kozlov, V.V.: Dynamical Systems X: General Theory of Vortices. Encyclopedia of Mathematical Sciences, vol.\u00a067. Springer, Berlin (2008)"},{"key":"9051_CR24","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1146\/annurev.fl.17.010185.002515","volume":"17","author":"A. Leonard","year":"1985","unstructured":"Leonard, A.: Computing three-dimensional incompressible flows with vortex elements. Annu. Rev. Fluid Mech. 17, 523\u2013559 (1985)","journal-title":"Annu. Rev. Fluid Mech."},{"key":"9051_CR25","unstructured":"Makhaldiani, N.: The system of three vortexes of two dimensional ideal hydrodynamics as a new example of the (integrable) Nambu\u2013Poisson mechanics. arXiv:solv-int\/9804002v1 (1998)"},{"key":"9051_CR26","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/0167-2789(83)90134-3","volume":"7","author":"J. Marsden","year":"1983","unstructured":"Marsden, J., Weinstein, A.: Coadjoint orbits, vortices and Clebsch variables for incompressible fluids. Physica D 7, 305\u2013323 (1983)","journal-title":"Physica D"},{"key":"9051_CR27","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1017\/S0022112086002744","volume":"167","author":"M.V. Melander","year":"1986","unstructured":"Melander, M.V., Zabusky, N.J., Styczek, A.S.: Moment model for vortex interactions. Part I. J. Fluid Mech. 167, 95\u2013115 (1986)","journal-title":"Part I. J. Fluid Mech."},{"key":"9051_CR28","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1017\/S0022112088002435","volume":"195","author":"M.V. Melander","year":"1988","unstructured":"Melander, M.V., Zabusky, N.J., McWilliams, J.C.: Symmetric vortex merger in two dimensions: causes and conditions. J. Fluid Mech. 195, 303\u2013340 (1988)","journal-title":"J. Fluid Mech."},{"key":"9051_CR29","doi-asserted-by":"crossref","first-page":"2405","DOI":"10.1103\/PhysRevD.7.2405","volume":"7","author":"Y. Nambu","year":"1973","unstructured":"Nambu, Y.: Generalized Hamiltonian mechanics. Phys. Rev. D 7, 2405\u20132412 (1973)","journal-title":"Phys. Rev. D"},{"key":"9051_CR30","doi-asserted-by":"crossref","first-page":"L1189","DOI":"10.1088\/0305-4470\/26\/22\/010","volume":"26","author":"P. Nevir","year":"1993","unstructured":"Nevir, P., Blender, R.: A Nambu representation of incompressible hydrodynamics using helicity and enstrophy. J. Phys. A, Math. Gen. 26, L1189\u2013L1193 (1993)","journal-title":"J. Phys. A, Math. Gen."},{"key":"9051_CR31","series-title":"Applied Mathematical Sciences","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-9290-3","volume-title":"The N-Vortex Problem: Analytical Techniques","author":"P.K. Newton","year":"2001","unstructured":"Newton, P.K.: The N-Vortex Problem: Analytical Techniques. Applied Mathematical Sciences, vol.\u00a0145. Springer, Berlin (2001)"},{"key":"9051_CR32","volume-title":"Th\u00e9orie des Tourbillons. Le\u00e7ons profes\u00e9es pendant le deuxi\u00e8me semestre 1891\u201392","author":"H. Poincar\u00e9","year":"1893","unstructured":"Poincar\u00e9, H.: Th\u00e9orie des Tourbillons. Le\u00e7ons profes\u00e9es pendant le deuxi\u00e8me semestre 1891\u201392. G.\u00a0Carre, Paris (1893) (available online at http:\/\/digital.library.cornell.edu\/cgi\/t\/text\/text-idx?c=math;idno=01800002 )"},{"key":"9051_CR33","series-title":"Cambridge Monographs on Mechanics and Applied Mathematics","volume-title":"Vortex Dynamics","author":"P.G. Saffman","year":"1992","unstructured":"Saffman, P.G.: Vortex Dynamics. Cambridge Monographs on Mechanics and Applied Mathematics. Cambridge University Press, Cambridge (1992)"},{"key":"9051_CR34","series-title":"Fluid Mechanics and its Applications","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/978-94-011-5042-2_8","volume-title":"IUTAM Symposium on Dynamics of Slender Vortices","author":"B.Yu. Scobelev","year":"1998","unstructured":"Scobelev, B.Yu., Shmagunov, O.A.: A new approach to the modeling viscous diffusion in vortex element methods. In: Krause, E., Gersten, K. (eds.) IUTAM Symposium on Dynamics of Slender Vortices. Fluid Mechanics and its Applications, pp.\u00a095\u2013104. Kluwer Academic, Dordrecht (1998)"},{"key":"9051_CR35","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/BF02103278","volume":"160","author":"L. Takhtajan","year":"1994","unstructured":"Takhtajan, L.: On foundation of the generalized Nambu mechanics. Commun. Math. Phys. 160, 295\u2013315 (1994)","journal-title":"Commun. Math. Phys."},{"key":"9051_CR36","series-title":"Lecture Notes in Physics","volume-title":"Viscous Vortical Flows","author":"L. Ting","year":"1991","unstructured":"Ting, L., Klein, R.: Viscous Vortical Flows. Lecture Notes in Physics, vol.\u00a0374. Springer, Berlin (1991)"},{"key":"9051_CR37","volume-title":"The Kinematics of Vorticity","author":"C. Truesdell","year":"1954","unstructured":"Truesdell, C.: The Kinematics of Vorticity. Indiana University Press, Bloomington (1954)"},{"key":"9051_CR38","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1088\/0951-7715\/5\/2\/008","volume":"5","author":"B.W. Fliert van\u00a0de","year":"1992","unstructured":"van\u00a0de Fliert, B.W., van Groesen, E.: Monopolar vortices as relative equilibria and their dissipative decay. Nonlinearity 5, 473\u2013495 (1992)","journal-title":"Nonlinearity"}],"container-title":["Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-009-9051-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00332-009-9051-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-009-9051-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,28]],"date-time":"2019-05-28T12:08:51Z","timestamp":1559045331000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00332-009-9051-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,10,10]]},"references-count":38,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,2]]}},"alternative-id":["9051"],"URL":"https:\/\/doi.org\/10.1007\/s00332-009-9051-4","relation":{},"ISSN":["0938-8974","1432-1467"],"issn-type":[{"value":"0938-8974","type":"print"},{"value":"1432-1467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,10,10]]}}}