Physics
Scientific paper
Dec 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007agufmsh23a1148k&link_type=abstract
American Geophysical Union, Fall Meeting 2007, abstract #SH23A-1148
Physics
7833 Mathematical And Numerical Techniques (0500, 3200)
Scientific paper
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.
Ko Che Ming
Ratkiewicz R. E.
Webb Gary M.
Zank Gary P.
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