M de Montigny et al 2003 J. Phys. A: Math. Gen. 36 2009 doi:10.1088/0305-4470/36/8/301
M de Montigny1,2, F C Khanna2,3 and A E Santana2,4
Show affiliationsWe use a geometrical formalism of Galilean invariance to build various hydrodynamics models. It consists in embedding the Newtonian spacetime into a non-Euclidean 4 + 1 space and provides thereby a procedure that unifies models otherwise apparently unrelated. After expressing the Navier–Stokes equation within this framework, we show that slight modifications of its Lagrangian allow us to recover the Chaplygin equation of state as well as models of superfluids for liquid helium (with both its irrotational and rotational components). Other fluid equations are also expressed in a covariant form.
47.85.Dh Hydrodynamics, hydraulics, hydrostatics
47.10.-g General theory in fluid dynamics
47.37.+q Hydrodynamic aspects of superfluidity; quantum fluids
76Y05 Quantum hydrodynamics and relativistic hydrodynamics (See also 83C55, 85A30)
76A25 Superfluids (classical aspects)
76D05 Navier-Stokes equations (See also 35Q30)
76Nxx Compressible fluids and gas dynamics, general
81Txx Quantum field theory; related classical field theories (See also 70Sxx)
Issue 8 (28 February 2003)
Received 20 August 2002
Published 12 February 2003
M de Montigny et al 2003 J. Phys. A: Math. Gen. 36 2009
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