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Volumn 463, Issue 2086, 2007, Pages 2671-2687

Multisymplectic formulation of fluid dynamics using the inverse map

Author keywords

Conservation laws; Fluid dynamics; Multisymplectic systems; Partial differential equations; Potential vorticity

Indexed keywords


EID: 36348964885     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2007.1892     Document Type: Article
Times cited : (47)

References (20)
  • 1
    • 0042137401 scopus 로고    scopus 로고
    • Multi-symplectic structures and wave propagation
    • doi:10.1017/ S0305004196001429
    • Bridges, T. J. 1997 Multi-symplectic structures and wave propagation. Math. Proc. Camb. Philos. Soc. 121, 147-190. (doi:10.1017/ S0305004196001429)
    • (1997) Math. Proc. Camb. Philos. Soc , vol.121 , pp. 147-190
    • Bridges, T.J.1
  • 2
    • 0037832748 scopus 로고    scopus 로고
    • ulti-symplectic integrators: Numerical schemes for Hamiltonian PDEs that preserve symplecticity
    • doi:10.1016/S0375-9601(01)00294-8
    • Bridges, T. J.&Reich, S. 2001Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that preserve symplecticity. Phys. Lett. A 284, 184-193. (doi:10.1016/S0375-9601(01)00294-8)
    • (2001) Phys. Lett. A , vol.284 , pp. 184-193
    • Bridges, T.J.1    Reich, S.2
  • 3
    • 22244442343 scopus 로고    scopus 로고
    • Multi-symplectic integrators: Numerical schemes for Hamiltonian PDEs that preserve symplecticity
    • doi:10.1088/0305-4470/38/6/015
    • Bridges, T. J., Hydon, P. E. & Reich, S. 2005 Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that preserve symplecticity. J. Phys. A 38, 1403-1418. (doi:10.1088/0305-4470/38/6/015)
    • (2005) J. Phys. A , vol.38 , pp. 1403-1418
    • Bridges, T.J.1    Hydon, P.E.2    Reich, S.3
  • 4
    • 12044254491 scopus 로고
    • An integrable shallow-water equation with peaked solitons
    • doi:10.1103/PhysRevLett.71.1661
    • Camassa, R. & Holm, D. D. 1993 An integrable shallow-water equation with peaked solitons. Phys. Rev. Lett. 71, 1661-1664. (doi:10.1103/PhysRevLett.71.1661)
    • (1993) Phys. Rev. Lett , vol.71 , pp. 1661-1664
    • Camassa, R.1    Holm, D.D.2
  • 5
    • 0034094180 scopus 로고    scopus 로고
    • Clebsch representation near points where the vorticity vanishes
    • doi:10.1063/1.870331
    • Graham, C. R. & Henyey, F. S. 2000 Clebsch representation near points where the vorticity vanishes. Phys. Fluids 12, 744-746. (doi:10.1063/1.870331)
    • (2000) Phys. Fluids , vol.12 , pp. 744-746
    • Graham, C.R.1    Henyey, F.S.2
  • 6
    • 0020733812 scopus 로고
    • Poisson brackets and Clebsch representations for magnetohydrodynamics, multifluid plasmas, and elasticity
    • doi:10.1016/0167-2789(83)90017-9
    • Holm, D. D. & Kupershmidt, B. 1983 Poisson brackets and Clebsch representations for magnetohydrodynamics, multifluid plasmas, and elasticity. Physica D 6, 347-363. (doi:10.1016/0167-2789(83)90017-9)
    • (1983) Physica D , vol.6 , pp. 347-363
    • Holm, D.D.1    Kupershmidt, B.2
  • 7
    • 35048836871 scopus 로고    scopus 로고
    • Momentum maps and measure valued solutions (peakons, filaments, and sheets) of the Euler-Poincaré equations for the diffeomorphism group
    • eds J. E. Marsden & T. S. Ratiu, pp, Boston, MA: Birkhäuser
    • Holm, D. D. & Marsden, J. E. 2004 Momentum maps and measure valued solutions (peakons, filaments, and sheets) of the Euler-Poincaré equations for the diffeomorphism group. In The breadth of symplectic and Poisson geometry: a Festshrift for Alan Weinstein (eds J. E. Marsden & T. S. Ratiu), pp. 203-235. Boston, MA: Birkhäuser http://arxiv.org/abs/ nlin.CD/0312048.
    • (2004) The breadth of symplectic and Poisson geometry: A Festshrift for Alan Weinstein , pp. 203-235
    • Holm, D.D.1    Marsden, J.E.2
  • 8
    • 0007080771 scopus 로고
    • The Hamiltonian structure of continuum mechanics in material inverse material, spatial and convective representations
    • eds D. D. Holm, J. E. Marsden & T. S. Ratiu, pp, Montreal, Canada: University of Montreal Press
    • Holm, D. D., Marsden, J. E. & Ratiu, T. S. 1986 The Hamiltonian structure of continuum mechanics in material inverse material, spatial and convective representations. In Hamiltonian structure and Lyapunov stability for ideal continuum dynamics (eds D. D. Holm, J. E. Marsden & T. S. Ratiu), pp. 1-124. Montreal, Canada: University of Montreal Press.
    • (1986) Hamiltonian structure and Lyapunov stability for ideal continuum dynamics , pp. 1-124
    • Holm, D.D.1    Marsden, J.E.2    Ratiu, T.S.3
  • 9
    • 0001971504 scopus 로고    scopus 로고
    • The Euler-Poincaré equations and semidirect products with applications to continuum theories
    • 1-81. See
    • Holm, D. D., Marsden, J. E. & Ratiu, T. S. 1998 The Euler-Poincaré equations and semidirect products with applications to continuum theories. Adv. Math. 137, 1-81. See http://arxiv.org/ abs/chao-dyn/9801015.
    • (1998) Adv. Math , vol.137
    • Holm, D.D.1    Marsden, J.E.2    Ratiu, T.S.3
  • 10
    • 7044241354 scopus 로고    scopus 로고
    • Soliton dynamics in computational anatomy
    • 170-178. See
    • Holm, D. D., Rananather, J. T., Trouvé, A. & Younes, L. 2004 Soliton dynamics in computational anatomy. NeuroImage 23, 170-178. See http://arxiv.org/abs/nlin.SI/0411014.
    • (2004) NeuroImage , vol.23
    • Holm, D.D.1    Rananather, J.T.2    Trouvé, A.3    Younes, L.4
  • 11
    • 22244479327 scopus 로고    scopus 로고
    • Multisymplectic conservation laws for differential and differential-difference equations
    • doi:10.1098/rspa.2004.1444
    • Hydon, P. E. 2005 Multisymplectic conservation laws for differential and differential-difference equations. Proc. R. Soc. A 461, 1627-1637. (doi:10.1098/rspa.2004.1444)
    • (2005) Proc. R. Soc. A , vol.461 , pp. 1627-1637
    • Hydon, P.E.1
  • 12
    • 36348989168 scopus 로고    scopus 로고
    • An overview of variational integrators
    • eds L. P. Franca, T. E. Tezduyar & A. Masud, pp, Barcelona, Spain: CIMNE
    • Lew, A., Marsden, J. E., Ortiz, M. & West, M. 2004 An overview of variational integrators. In Finite element methods: 1970s and beyond (eds L. P. Franca, T. E. Tezduyar & A. Masud), pp. 98-115. Barcelona, Spain: CIMNE.
    • (2004) Finite element methods: 1970s and beyond , pp. 98-115
    • Lew, A.1    Marsden, J.E.2    Ortiz, M.3    West, M.4
  • 14
    • 48749149748 scopus 로고
    • Coadjoint orbits, vortices, and Clebsch variables for incompressible fluids
    • doi:10.1016/0167-2789(83)90134-3
    • Marsden, J. E. & Weinstein, A. 1983 Coadjoint orbits, vortices, and Clebsch variables for incompressible fluids. Physica D 7, 305-323. (doi:10.1016/0167-2789(83)90134-3)
    • (1983) Physica D , vol.7 , pp. 305-323
    • Marsden, J.E.1    Weinstein, A.2
  • 15
    • 0000140852 scopus 로고    scopus 로고
    • Variational methods, multisymplectic geometry and continuum mechanics
    • doi:10.1016/S0393-0440(00)00066-8
    • Marsden, J., Pekarsky, S., Shkoller, S. & West, M. 2001 Variational methods, multisymplectic geometry and continuum mechanics. J. Geom. Phys. 38, 253-284. (doi:10.1016/S0393-0440(00)00066-8)
    • (2001) J. Geom. Phys , vol.38 , pp. 253-284
    • Marsden, J.1    Pekarsky, S.2    Shkoller, S.3    West, M.4
  • 16
    • 0036403673 scopus 로고    scopus 로고
    • On the metrics and Euler-Lagrange equations of computational anatomy
    • doi:10.1146/annurev.bioeng.4.092101.125733
    • Miller, M. I., Trouvé, A. & Younes, L. 2002 On the metrics and Euler-Lagrange equations of computational anatomy. Annu. Rev. Biomed. Eng. 4, 375-405. (doi:10.1146/annurev.bioeng.4.092101.125733)
    • (2002) Annu. Rev. Biomed. Eng , vol.4 , pp. 375-405
    • Miller, M.I.1    Trouvé, A.2    Younes, L.3
  • 17
    • 22244438583 scopus 로고    scopus 로고
    • The circulation density and its role in 3D turbulence
    • doi:10.1016/S0167-2789(96) 00180-7
    • Nazarenko, S. V. 1997 The circulation density and its role in 3D turbulence. Physica D 102, 343-348. (doi:10.1016/S0167-2789(96) 00180-7)
    • (1997) Physica D , vol.102 , pp. 343-348
    • Nazarenko, S.V.1
  • 18
    • 0002142650 scopus 로고
    • Variational principles in continuum mechanics
    • doi:10.1098/rspa.1968.0103
    • Seliger, R. L. & Whitham, G. B. 1968 Variational principles in continuum mechanics. Proc. R. Soc. A 305, 1-25. (doi:10.1098/rspa.1968.0103)
    • (1968) Proc. R. Soc. A , vol.305 , pp. 1-25
    • Seliger, R.L.1    Whitham, G.B.2
  • 19
    • 0000286944 scopus 로고
    • Mathematical principles of classical fluid mechanics
    • eds S. Flügge & C. Truesdell, pp, Berlin, Germany: Springer
    • Serrin, J. 1959 Mathematical principles of classical fluid mechanics. In Handbuch der Physik VIII/I (eds S. Flügge & C. Truesdell), pp. 125-263. Berlin, Germany: Springer.
    • (1959) Handbuch der Physik VIII/I , pp. 125-263
    • Serrin, J.1
  • 20
    • 4243329996 scopus 로고    scopus 로고
    • Hidden conservation laws in hydrodynamics, energy and dissipation rate fluctuation spectra in strong turbulence
    • doi:10.1016/0167-2789(93) 90050-B
    • Yakhot, V. & Zakharov, V. 1997 Hidden conservation laws in hydrodynamics, energy and dissipation rate fluctuation spectra in strong turbulence. Physica D 64, 379-394. (doi:10.1016/0167-2789(93) 90050-B)
    • (1997) Physica D , vol.64 , pp. 379-394
    • Yakhot, V.1    Zakharov, V.2


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