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The Incompressible Non-Relativistic Navier-Stokes Equation from Gravity · Around

2008

The Incompressible Non-Relativistic Navier-Stokes Equation from Gravity

Bhattacharyya, Sayantani, Minwalla, Shiraz, Wadia, Spenta R.

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We note that the equations of relativistic hydrodynamics reduce to the incompressible Navier-Stokes equations in a particular scaling limit.

In this limit boundary metric fluctuations of the underlying relativistic system turn into a forcing function identical to the action of a background electromagnetic field on the effectively charged fluid.
We demonstrate that special conformal symmetries of the parent relativistic theory descend to `accelerated boost' symmetries of the Navier-Stokes equations, uncovering a possibly new conformal symmetry structure of these equations.
Applying our scaling limit to holographically induced fluid dynamics, we find gravity dual descriptions of an arbitrary solution of the forced non-relativistic incompressible Navier-Stokes equations.

Built on

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L. D. Landau and E. M. Lifshitz, Fluid mechanics · 1959
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V. N. Gusyatnikova and V. A. Yumaguzhin, Symmetries and conservation laws of navier-stokes equations
1989
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J. M. Maldacena, The large N limit of superconformal field theories and supergravity
1998
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L. O’Raifeartaigh and V. V. Sreedhar, The maximal kinematical invariance group of fluid dynamics and explosion-implosion duality
2001
Earlier work this paper cites.

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