The geometry and analysis of the averaged Euler equations and a new diffeomorphism group
We present a geometric analysis of the incompressible averaged Euler equations for an ideal inviscid fluid. We show that solutions of these equations are geodesics on the volume-preserving diffeomorphism group of a new weak right invariant pseudo metric. We prove that for precompact open subsets of...
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| Format: | Journal article |
| Language: | English |
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1999
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| _version_ | 1797080550120357888 |
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| author | Marsden, J Ratiu, T Shkoller, S |
| author_facet | Marsden, J Ratiu, T Shkoller, S |
| author_sort | Marsden, J |
| collection | OXFORD |
| description | We present a geometric analysis of the incompressible averaged Euler equations for an ideal inviscid fluid. We show that solutions of these equations are geodesics on the volume-preserving diffeomorphism group of a new weak right invariant pseudo metric. We prove that for precompact open subsets of ${\mathbb R}^n$, this system of PDEs with Dirichlet boundary conditions are well-posed for initial data in the Hilbert space $H^s$, $s>n/2+1$. We then use a nonlinear Trotter product formula to prove that solutions of the averaged Euler equations are a regular limit of solutions to the averaged Navier-Stokes equations in the limit of zero viscosity. This system of PDEs is also the model for second-grade non-Newtonian fluids. |
| first_indexed | 2024-03-07T01:01:44Z |
| format | Journal article |
| id | oxford-uuid:89f3a6a5-565c-4a6d-8e59-ee2b1d2c66fa |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T01:01:44Z |
| publishDate | 1999 |
| record_format | dspace |
| spelling | oxford-uuid:89f3a6a5-565c-4a6d-8e59-ee2b1d2c66fa2022-03-26T22:28:08ZThe geometry and analysis of the averaged Euler equations and a new diffeomorphism groupJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:89f3a6a5-565c-4a6d-8e59-ee2b1d2c66faEnglishSymplectic Elements at Oxford1999Marsden, JRatiu, TShkoller, SWe present a geometric analysis of the incompressible averaged Euler equations for an ideal inviscid fluid. We show that solutions of these equations are geodesics on the volume-preserving diffeomorphism group of a new weak right invariant pseudo metric. We prove that for precompact open subsets of ${\mathbb R}^n$, this system of PDEs with Dirichlet boundary conditions are well-posed for initial data in the Hilbert space $H^s$, $s>n/2+1$. We then use a nonlinear Trotter product formula to prove that solutions of the averaged Euler equations are a regular limit of solutions to the averaged Navier-Stokes equations in the limit of zero viscosity. This system of PDEs is also the model for second-grade non-Newtonian fluids. |
| spellingShingle | Marsden, J Ratiu, T Shkoller, S The geometry and analysis of the averaged Euler equations and a new diffeomorphism group |
| title | The geometry and analysis of the averaged Euler equations and a new
diffeomorphism group |
| title_full | The geometry and analysis of the averaged Euler equations and a new
diffeomorphism group |
| title_fullStr | The geometry and analysis of the averaged Euler equations and a new
diffeomorphism group |
| title_full_unstemmed | The geometry and analysis of the averaged Euler equations and a new
diffeomorphism group |
| title_short | The geometry and analysis of the averaged Euler equations and a new
diffeomorphism group |
| title_sort | geometry and analysis of the averaged euler equations and a new diffeomorphism group |
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