(adsbygoogle = window.adsbygoogle || []).push({}); Continuum approximation of fluid mechanics (& relativistic fluids)

I have a few 'foundational' questions on fluid mechanics which I haven't been able to find quick answers to, any help would be appreciated.

At the start of any course on fluids, one is told of the continuum [STRIKE]hypothesis[/STRIKE] approximation - at large particle numbers and large enough distance scales, the atomic degrees of freedom become irrelevant and the fluid can be accurately modeled by a continuum.

Q1) Can one start from a microscopic theory and recover the Navier-Stokes equations in the appropriate limit? I know there are some attempts at this - but is there a consensus on the correct way to do it?

Q2) If one wishes to describe a relativistic fluid, can one make a continuum hypothesis ( since lengths are not Lorentz invariant) ? I know that relativistic fluid equations are used to describe e.g. neutron stars. Surely some inertial observers would not see a continuum, and would have to use a microscopic theory to describe the fluid... this seems like it could lead to inconsistencies?

Thanks.

[EDIT] Changed title from ...continuum hypothesis... to ...continuum approximation... .

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Continuum hypothesis of fluid mechanics (& relativistic fluids)

**Physics Forums | Science Articles, Homework Help, Discussion**