Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global Existence of Strong and Weak Solutions to 2D Compressible
  Navier-Stokes System in Bounded Domains with Large Data and Vacuum   We study the barotropic compressible Navier-Stokes system where the shear
viscosity is a positive constant and the bulk one proportional to a power of
the density with the power bigger than one and a third. The system is subject
to the Navier-slip boundary conditions in a general two-dimensional bounded
simply connected domain. For initial density allowed to vanish, we establish
the global existence of strong and weak solutions without any restrictions on
the size of initial value. To get over the difficulties brought by boundary, on
the one hand, we apply Riemann mapping theorem and the pull back Green's
function method to get a pointwise representation of the effective viscous
flux. On the other hand, observing that the orthogonality is preserved under
conformal mapping due to its preservation on the angle, we use the slip
boundary conditions to reduce the integral representation to the desired
commutator form whose singularities can be cancelled out by using the estimates
on the spatial gradient of the velocity.

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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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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: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga