Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetric forms for hyperbolic-parabolic systems of multi-gradient
  fluids   We consider multi-gradient fluids endowed with a volumetric internal energy
which is a function of mass density, volumetric entropy and their successive
gradients. We obtained the thermodynamic forms of equation of motions and
equation of energy, and the motions are compatible with the two laws of
thermodynamics. The equations of multi-gradient fluids belong to the class of
dispersive systems. In the conservative case, we can replace the set of
equations by a quasi-linear system written in a divergence form. Near an
equilibrium position, we obtain a symmetric-Hermitian system of equations in
the form of Godunov's systems. The equilibrium positions are proved to be
stable when the total volume energy of the fluids is a convex function with
respect to convenient conjugated variables-called main field-of mass density,
volumetric entropy, their successive gradients, and velocity.

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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol