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A Covariant Form of the Navier-Stokes Equation for the Galilean Conformal Algebra | | Ayan Mukhopadhyay
; | | Date: |
6 Aug 2009 | | Abstract: | We demonstrate that the Navier-Stokes equation can be covarantized under the
full infinite dimensional Galilean Conformal Algebra (GCA), such that it
reduces to the usual Navier-Stokes equation in an inertial frame. The
covariantization is possible only for incompressible flows, i.e. when the
divergence of the velocity field vanishes. Using the continuity equation, we
can fix the transformation of the pressure and density under GCA uniquely. We
also find that when all chemical potentials vanish, $c_{s}$, which denotes the
speed of sound in an inertial frame comoving with the flow, must either be a
fundamental constant or given in terms of microscopic parameters. We will
discuss how both could be possible. In absence of chemical potentials, we also
find that the covariance under GCA implies that either the viscosity should
vanish or the microscopic theory should have a length scale or a time scale or
both. We argue that we can be open to the later possibility. Finally, we see
that the higher derivative corrections to the Naver-Stokes equation, can be
covariantized, only if they are restricted to certain possible combinations in
the inertial frame. We explicitly evaluate all possible three derivative
corrections. | | Source: | arXiv, 0908.0797 | | Services: | Forum | Review | PDF | Favorites | |
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