>>14354545'rev' means representative elementary volume. So basically exactly what you said, you take some 'small' region of the fluid and then derive some conservation laws over it, this yields the PDE.
>It makes no sense to say that the equation has to be 'true in a mathematical sense' in the same way you can't say that for F = ma.Yes this is exactly my point, sure, you can argue that the equation is true in a physical sense, as in it accurately describes the physics its trying to model. However, from a mathematical perspective saying the equation is "true" is utter nonsense, that is, unless you're talking about well posedness.
