메뉴 건너뛰기




Volumn 97, Issue 1, 2011, Pages 45-60

Generalized Euler-Poincaré Equations on Lie Groups and Homogeneous Spaces, Orbit Invariants and Applications

Author keywords

Cauchy problem; Euler Poincar equation; homogeneous space; well posedness

Indexed keywords


EID: 79956143369     PISSN: 03779017     EISSN: 15730530     Source Type: Journal    
DOI: 10.1007/s11005-011-0464-2     Document Type: Article
Times cited : (26)

References (24)
  • 3
    • 34250136481 scopus 로고
    • Remarks on the breakdown of smooth solutions for the 3-D Euler equations
    • Beale J. T., Kato T., Majda A.: Remarks on the breakdown of smooth solutions for the 3-D Euler equations. Commun. Math. Phys. 94, 61-66 (1984).
    • (1984) Commun. Math. Phys. , vol.94 , pp. 61-66
    • Beale, J.T.1    Kato, T.2    Majda, A.3
  • 4
    • 12044254491 scopus 로고
    • An integrable shallow water equation with peaked solitons
    • Camassa R., Holm D. D.: An integrable shallow water equation with peaked solitons. Phys. Rev. Lett. 71, 1661-1664 (1993).
    • (1993) Phys. Rev. Lett. , vol.71 , pp. 1661-1664
    • Camassa, R.1    Holm, D.D.2
  • 7
    • 0001052255 scopus 로고
    • Groups of diffeomorphisms and the motion of an incompressible fluid
    • Ebin D., Marsden J.: Groups of diffeomorphisms and the motion of an incompressible fluid. Ann. Math. 92, 102-163 (1970).
    • (1970) Ann. Math. , vol.92 , pp. 102-163
    • Ebin, D.1    Marsden, J.2
  • 8
    • 81555201634 scopus 로고    scopus 로고
    • The Degasperis-Procesi equation as a non-metric Euler equation
    • doi: 10. 1007/s00209-010-0778-2
    • Escher, J., Kolev, B.: The Degasperis-Procesi equation as a non-metric Euler equation. Math. Z. doi: 10. 1007/s00209-010-0778-2 (2009).
    • (2009) Math. Z
    • Escher, J.1    Kolev, B.2
  • 9
    • 84998547969 scopus 로고    scopus 로고
    • Momentum maps and measure-valued solutions (peakons, filaments and sheets) for the EPDiff equation
    • Holm D., Marsden J. E.: Momentum maps and measure-valued solutions (peakons, filaments and sheets) for the EPDiff equation. Progr. Math. 232, 203-235 (2004).
    • (2004) Progr. Math. , vol.232 , pp. 203-235
    • Holm, D.1    Marsden, J.E.2
  • 10
    • 0001971504 scopus 로고    scopus 로고
    • The Euler-Poincaré equations and semidirect products with applications to continuum theories
    • Holm D., Marsden J., Ratiu T.: The Euler-Poincaré equations and semidirect products with applications to continuum theories. Adv. Math. 137, 1-81 (1997).
    • (1997) Adv. Math. , vol.137 , pp. 1-81
    • Holm, D.1    Marsden, J.2    Ratiu, T.3
  • 11
  • 12
    • 33746373002 scopus 로고    scopus 로고
    • Geometrical theory of dynamical systems and fluid flows
    • World Scientific, Singapore
    • Kambe, T.: Geometrical theory of dynamical systems and fluid flows. In: Advanced Series in Nonlinear Dynamics, vol. 23. World Scientific, Singapore (2004).
    • (2004) Advanced Series in Nonlinear Dynamics , vol.23
    • Kambe, T.1
  • 13
    • 0037612018 scopus 로고    scopus 로고
    • Euler equations on homogeneous spaces and Virasoro orbits
    • Khesin B., Misiołek G.: Euler equations on homogeneous spaces and Virasoro orbits. Adv. Math. 176, 116-144 (2003).
    • (2003) Adv. Math. , vol.176 , pp. 116-144
    • Khesin, B.1    Misiołek, G.2
  • 14
    • 50849122333 scopus 로고    scopus 로고
    • Generalized Hunter-Saxton equation and geometry of the circle diffeomorphism group
    • Khesin B., Lenells J., Misiołek G.: Generalized Hunter-Saxton equation and geometry of the circle diffeomorphism group. Math. Ann. 342, 617-656 (2008).
    • (2008) Math. Ann. , vol.342 , pp. 617-656
    • Khesin, B.1    Lenells, J.2    Misiołek, G.3
  • 15
    • 35748939866 scopus 로고    scopus 로고
    • The geometry of infinite-dimensional groups
    • Springer, New York
    • Khesin, B., Wendt, R.: The geometry of infinite-dimensional groups. Ergebnisse der Mathematik, vol. 51. Springer, New York (2008).
    • (2008) Ergebnisse der Mathematik , vol.51
    • Khesin, B.1    Wendt, R.2
  • 17
    • 77955550646 scopus 로고    scopus 로고
    • Integrable evolution equations on spaces of tensor densities and their peakon solutions
    • Lenells J., Misiołek G., Ti{dotless}ǧlay F.: Integrable evolution equations on spaces of tensor densities and their peakon solutions. Commun. Math. Phys. 299, 129-161 (2010).
    • (2010) Commun. Math. Phys. , vol.299 , pp. 129-161
    • Lenells, J.1    Misiołek, G.2    Tiǧlay, F.3
  • 19
    • 0001168352 scopus 로고
    • The reduced Euler-Lagrange equations
    • Marsden J. E., Scheurle J.: The reduced Euler-Lagrange equations. Fields Inst. Comm. 1, 139-164 (1993).
    • (1993) Fields Inst. Comm. , vol.1 , pp. 139-164
    • Marsden, J.E.1    Scheurle, J.2
  • 20
    • 0036436154 scopus 로고    scopus 로고
    • Classical solutions of the periodic Camassa-Holm equation
    • Misiołek G.: Classical solutions of the periodic Camassa-Holm equation. Geom. Funct. Anal. 12, 1080-1104 (2002).
    • (2002) Geom. Funct. Anal. , vol.12 , pp. 1080-1104
    • Misiołek, G.1
  • 21
    • 77951203607 scopus 로고    scopus 로고
    • Fredholm properties of Riemannian exponential maps on diffeomorphism groups
    • Misiołek G., Preston S. C.: Fredholm properties of Riemannian exponential maps on diffeomorphism groups. Invent. Math. 179, 191-227 (2010).
    • (2010) Invent. Math. , vol.179 , pp. 191-227
    • Misiołek, G.1    Preston, S.C.2
  • 22
    • 6344247445 scopus 로고    scopus 로고
    • Coadjoint representation of Virasoro-type Lie algebras and differential operators on tensor-densities
    • Birkhauser, Basel
    • Ovsienko, V.: Coadjoint representation of Virasoro-type Lie algebras and differential operators on tensor-densities. DMV Sem. vol. 31, pp. 231-255. Birkhauser, Basel (2001).
    • (2001) DMV Sem , vol.31 , pp. 231-255
    • Ovsienko, V.1
  • 23
    • 0003203437 scopus 로고
    • Pseudodifferential operators and nonlinear PDE
    • Birkhäuser, Boston
    • Taylor, M. E.: Pseudodifferential operators and nonlinear PDE. In: Progress in Mathematics, vol. 100. Birkhäuser, Boston (1991).
    • (1991) Progress in Mathematics , vol.100
    • Taylor, M.E.1
  • 24
    • 83055180412 scopus 로고    scopus 로고
    • Geodesic equations on diffeomorphism groups
    • Vizman C.: Geodesic equations on diffeomorphism groups. SIGMA 4, 030 (2008).
    • (2008) Sigma , vol.4 , pp. 030
    • Vizman, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.