Editing Appendix/Ramblings/Radiation/RadHydro (section)

===Hayes et al. (2006) &#8212; But Ignoring the Effects of Magnetic Fields===
First, referencing &sect;2 of {{ ZEUS-MP2006full }} &#8212; alternatively see &sect;2.1 of {{ MT2012full }} &#8212; we see that the set of principal governing equations that is typically used in the astrophysics community to include the effects of radiation on self-gravitating fluid flows includes the,
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<span id="Poisson"><font color="#770000">'''Poisson Equation'''</font></span>

{{ Math/EQ_Poisson01 }}

{{ ZEUS-MP2006 }}, p. 190, Eq. (15)
</div>
the,
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<span id="Continuity"><font color="#770000">'''Continuity Equation'''</font></span>

{{ Math/EQ_Continuity01 }}
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and &#8212; ignoring magnetic fields &#8212; a modified version of the, 

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<span id="ConservingMomentum:Lagrangian"><font color="#770000">'''Lagrangian Representation'''</font></span><br />
of the Euler Equation,
<table border="0" cellpadding="5" align="center">

<tr>
  <td align="right">
<math>\frac{d\vec{v}}{dt}</math>
  </td>
  <td align="center">
<math>=</math>
  </td>
  <td align="left">
<math>
- \frac{1}{\rho}\nabla P - \nabla \Phi + \frac{1}{\rho}\biggl(\frac{\chi}{c}\biggr) \vec{F} \, ,
</math>
  </td>
</tr>
</table>
</div>
plus the following pair of additional ''energy-conservation-based'' dynamical equations:
<table border="0" cellpadding="5" align="center">

<tr>
  <td align="right">
<math>\rho \frac{d}{dt} \biggl( \frac{e}{\rho}\biggr) + P\nabla \cdot \vec{v} </math>
  </td>
  <td align="center">
<math>=</math>
  </td>
  <td align="left">
<math>
c\kappa_E E_\mathrm{rad} - 4\pi \kappa_p B_p \, ,
</math>
  </td>
</tr>

<tr>
  <td align="right">
<math>\rho \frac{d}{dt} \biggl( \frac{E_\mathrm{rad}}{\rho}\biggr)</math>
  </td>
  <td align="center">
<math>=</math>
  </td>
  <td align="left">
<math>
- \biggl[ \nabla \cdot \vec{F} + \bold{P}_\mathrm{st}:\nabla{\vec{v}} + c\kappa_E E_\mathrm{rad} - 4\pi \kappa_p B_p \biggr]  \, ,
</math>
  </td>
</tr>
</table>
where, in this last expression, <math>\bold{P}_\mathrm{st}</math> is the radiation stress tensor.