Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global Existence of Weak Solutions for Compresssible Navier--Stokes
  Equations: Thermodynamically unstable pressure and anisotropic viscous stress
  tensor   We prove global existence of appropriate weak solutions for the compressible
Navier--Stokes equations for more general stress tensor than those covered by
P.-L. Lions and E. Feireisl's theory. More precisely we focus on more general
pressure laws which are not thermodynamically stable; we are also able to
handle some anisotropy in the viscous stress tensor. To give answers to these
two longstanding problems, we revisit the classical compactness theory on the
density by obtaining precise quantitative regularity estimates: This requires a
more precise analysis of the structure of the equations combined to a novel
approach to the compactness of the continuity equation. These two cases open
the theory to important physical applications, for instance to describe solar
events (virial pressure law), geophysical flows (eddy viscosity) or biological
situations (anisotropy).

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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: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin