Astronomy and Astrophysics – Astrophysics
Scientific paper
Jun 1991
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991ap%26ss.180...19k&link_type=abstract
Astrophysics and Space Science (ISSN 0004-640X), vol. 180, no. 1, June 1991, p. 19-37.
Astronomy and Astrophysics
Astrophysics
Ideal Fluids, Lagrangian Equilibrium Points, Relativity, Rotating Fluids, Thermodynamic Equilibrium, Barotropic Flow, Compressible Fluids, Integral Equations, Liapunov Functions, Magnetic Fields
Scientific paper
The conditions for the self-gravitating configurations of an ideal fluid are developed theoretically, with particular attention given to velocity distribution and equilibrium, as well as contradictions relating to previous analyses. The integrals of motion for the continuum medium in previous work were not common to the material-points system which led to divergence using both Liapunov and Riemann approaches. After correcting the integrals of motion, the equilibrium conditions and velocity distributions are developed for a homogeneous fluid, a compressible fluid, a fluid with a magnetic field, and an ideal fluid in the post-Newtonian approximation of general relativity. The equilibrium conditions are found to be related to the presence of freezing-in vector fields based on scalar potentials, whose total derivative is equal to zero.
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