# Conformal symmetry of Navier-Stokes?

This question is in reference to the paper arXiv:0810.1545

• Can someone help understand this scaling argument and the proof(?) that there is a conformal symmetry in Navier-Stoke's equation? (..am I even reading the result right?..)

• Is one saying that the equations 3.4 encode the full symmetry of equation 1.1? If yes, how? What calculation do I need to do to check that?

I am unable to understand how to read 3.4

• Also what role does equation 2.9 play? Are the new symmetries specific to the form 2.9 or they apply to the general 1.1?

• Also 2.9 and 1.1 don't seem to be the "same" as apparently claimed- 2.9 has the time derivative of a0 and also a viscosity-Ricci term. What's going on?

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Would you please consider making this question self-contained? – user1504 Mar 20 '13 at 23:18
I've only read the paper very briefly, but note that NS itself is clearly not conformally invariant ($\nu$ is dimensionful). Minwalla + friends discuss a particular scaling limit, which should enjoy more symmetries. (3.4) defines how the vector $v^i = v^i(x,t)$ transforms (under infinitesimal transformations). They decompose the conformal group in some special non-relativistic way, but qualitatively there's nothing new (compared to the ordinary conformal group). – Vibert Mar 20 '13 at 23:20
Which rascal has downvoted this question ...?! Even though I agree that it would be much better to type the equations into the question, this is no reason to downvote, leaving a comment as user1504 did is enough! – Dilaton Mar 21 '13 at 0:11
@Vibert So how does one check that the 3.4 are the symmetries of the equation 1.1 in some scaling limit? May be you can heuristically sketch the checking calculation - like the steps by which one one proves that in some scaling limit (which one?) is 3.4 a symmetry of (1.1? 2.9?). – user6818 Mar 21 '13 at 20:55
@Anirbit: I'd love to help you out, but I have a finite amount of time to do so ;) and close-reading a paper I've never seen before would take hours... – Vibert Mar 21 '13 at 21:04