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| HAL: hal-00528726, version 1 |
| arXiv: 1010.4844 |
| DOI: 10.3934/cpaa.2012.11.1407 |
| Detailed view |  Export this paper |
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| Communications on Pure and Applied Analysis 11, 4 (2012) 1407 - 1419 |
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| The geometry of a vorticity model equation |
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| Joachim Escher 1Boris Kolev 2 |
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| (2012-07) |
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| We provide rigorous evidence of the fact that the modified Constantin-Lax-Majda equation modeling vortex and quasi-geostrophic dynamics describes the geodesic flow on the subgroup of orientation-preserving diffeomorphisms fixing one point, with respect to right-invariant metric induced by the homogeneous Sobolev norm $H^{1/2}$ and show the local existence of the geodesics in the extended group of diffeomorphisms of Sobolev class $H^{k}$ with $k\ge 2$. |
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| 1: | Institute for Applied Mathematics (IFAM) |
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Leibniz Universität Hannover |
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| 2: | Laboratoire d'Analyse, Topologie, Probabilités (LATP) |
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CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III |
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| 3: | Research Institute for Mathematical Sciences (RIMS) |
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Kyoto University |
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| Subject | : | Mathematics/Analysis of PDEs Physics/Mathematical Physics Mathematics/Mathematical Physics |
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| Constantin-Lax-Majda equation – Euler equation on diffeomorphisms group of the circle |
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| hal-00528726, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00528726 | |
| oai:hal.archives-ouvertes.fr:hal-00528726 | |
| From: Boris Kolev | |
| Submitted on: Friday, 22 October 2010 13:14:16 | |
| Updated on: Thursday, 23 February 2012 12:39:34 | |
