Abstract
An abstract dynamical system is formulated from three features extracted from classical hydrodynamics. One its particular realization is then the classical hydrodynamics, other possible realizations are extensions of the classical hydrodynamics. The three features entering the formulation of the abstract dynamical system are the conservation laws, the compatibility with equilibrium thermodynamics, and the compatibility with classical mechanics in the limit of no dissipation. The particular extensions on which we illustrate the process of constructing different realizations are those arising when dealing with fluids in the vicinity of gas-liquid phase transitions (i.e. fluids involving large spatial inhomogeneities and large fluctuations).
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Grmela, M. Extensions of Classical Hydrodynamics. J Stat Phys 132, 581–602 (2008). https://doi.org/10.1007/s10955-008-9558-3
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DOI: https://doi.org/10.1007/s10955-008-9558-3