Scaling Symmetries, Non-local Symmetries and Conservation Laws in 1D Gas Dynamics
Dr. Gary M. Webb
Center for Space Plasma and Aeronomic Research
September 11, 2009
219 Shelby Center
3:00 (Refreshements at 2:30)
The equations of gas dynamics and magnetohydrodynamics can be derived from Lagrangian variational principles. We briefly describe how this works for 1D gas dynamics. Scaling symmetry conservation laws in 1D gas dynamics are derived for the case of an adiabatic gas, with a constant adiabatic index, by a judicious combination of the three scaling symmetries and application of Noether's theorem. Using the approach of Sjoberg and Mahomed (2004) to non-local conservation laws and symmetries, we obtain a non-local conservation law associated with the scaling symmetries. A constrained variational principle for the Sjoberg and Mahomed cover system, consisting of known conservation laws, their pseudo-potentials and the original gas dynamic equations, is developed. The constrained variational principle is used to derive non-local conservation laws by means of Noether's theorem.
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