Which kinds of Physics laws do and don't comply with the principle of relativity?

In Physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference.

However, according to this and this paper, it seems Bernoulli's Equation is a frame-dependent example in both Newtonian and relativistic mechanics.

Which kinds of laws are frame-independent and which are not?

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What do you mean by 'kind of law'? Bernoulli's Equation isn't a law -- it's a simplification of the Euler equations under isentropic conditions. – tpg2114 Dec 23 '12 at 2:59
So your question is more "What makes a law frame independent?" I am really unclear on your question as it is written. – tpg2114 Dec 23 '12 at 3:26
Again -- do you mean to ask "What makes a law frame-independent?" By asking "What kinds of laws" implies you are looking for either a list of frame-dependent laws or something more vague like "Conservation" which also doesn't make sense. If you are interested in what constraints make something frame-dependent, you really need to re-write your question to clarify that. – tpg2114 Dec 23 '12 at 3:34
I think that the misunderstanding comes from the use of "law" in your question. A law in my vocabulary is "conservation of energy",etc. In this day and age in physics laws are called, by definition, those that ARE CONSISTENT with special relativity. All previous formulations, in Newtonian for example, that might have been called laws in the nineteenth century are out of date in physics as we know it presently. – anna v Dec 23 '12 at 4:44
@JohnRennie: Oops. I read this as "which law of physics" (narq) and not "which kind of law" (perfectly OK, and a good question imho). Reopened, thanks for noticing :) – Manishearth Dec 23 '12 at 14:20

All basic laws of physics are frame-independent. They either exhibit Galilean (non-relativistic) or Lorentzian (relativistic) invariance. Examples are Newton's laws (Galilean), Maxwell's equations (Lorentzian), Navier-Stokes equations (Galilean), etc. A notable exception is formed by Schrödinger's equation which, upon closer inspection, can be fixed into being Lorentz invariant under transformations up to first order in $v/c$.
these are two distinct symmetries which become indistinguishable in the limit $v/c -> 0$. – Johannes Dec 24 '12 at 12:05