HR: 1340h
AN: SH23A-1148    [Abstracts]
TI: The Lagrangian Map and Lie Symmetries in Magnetohydrodynamics and Gas Dynamics
AU: Ko, C M
EM: cmko@astro.ncu.edu.tw
AF: Department of Physics, Institute of Astronomy and Center for Complex Systems, National Central University, 300 Jung-da Rd., Taoyuan, Chung-Li, 32054, Taiwan
AU: * Webb, G M
EM: gmwebb@ucr.edu
AF: Institute of Geophysics and Planetary Physics, University of California Riverside, 900 University Ave., Riverside, CA 92521, United States
AU: Ratkiewicz, R E
EM: roma@cbk.waw.pl
AF: Space Research Center, Bartycka 18A, Warsaw, 00176, Poland
AU: Zank, G P
EM: zank@ucr.edu
AF: Institute of Geophysics and Planetary Physics, University of California Riverside, 900 University Ave., Riverside, CA 92521, United States
AB: We explore the role of the Lagrangian map for Lie symmetries in magnetohydrodynamics and gas dynamics. By converting the Eulerian Lie point symmetries of the Galilean group to Lagrange label space, in which the Eulerian position is regarded as a function of the Lagrange fluid label and time t, one finds that there is an infinite class of symmetries in Lagrange label space that map onto each Lie point symmetry. This involves the solution of the Lie determining equations for the fluid relabeling symmetries. We also consider a class of scaling symmetries for a gas with a constant adiabatic index. These symmetries map onto a modified form of the fluid relabeling symmetry determining equations with non-zero source terms. We investigate under what conditions the scaling symmetries give rise to conservation laws, and find that the conservation laws depend on the initial entropy, density and magnetic field of the fluid. Lie algebraic structures in Lagrange label space corresponding to the symmetries are investigated.
DE: 7833 Mathematical and numerical techniques (0500, 3200)
SC: SPA-Solar and Heliospheric Physics [SH]
MN: 2007 Fall Meeting