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**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... .

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