The Structure, Stability, and Dynamics
of Self-Gravitating Systems

Principal Governing Equations

According to Landau and Lifshitz's (1975) eloquent discussion of the broad subject of Fluid Mechanics1, the state of a moving fluid is determined by five quantities: the three components of the velocity v and, for example, the pressure P and the density r. For our discussions of astrophysical fluid systems throughout this Hypertext Book [H_Book], we will add to this the gravitational potential F. Accordingly, a complete system of equations of fluid dynamics should be six in number. For an ideal fluid these are:

Euler's Equation
(The Vector Equation of Motion)

Dv = - (1/r)P - F

Equation of Continuity
(Mass Conservation)

Dr + r v = 0

Adiabatic Form of the
First Law of Thermodynamics
(Specific Entropy Conservation)

De + P D(1/r) = 0

Poisson Equation

2F = 4p Gr .

1Text in green is taken verbatim from Chapter I, $#167; 2 of Landau and Lifshitz's Fluid Mechanics (1975).