Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Steady solutions to viscous shallow water equations. The case of heavy
  water   In this note, we show the existence of regular solutions to the stationary
version of the Navier-Stokes system for compressible fluids with a density
dependent viscosity, known as the shallow water equations. For arbitrary large
forcing we are able to construct a solution, provided the total mass is
sufficiently large. The main mathematical part is located in the construction
of solutions. Uniqueness is impossible to obtain, since the gradient of the
velocity is of magnitude of the force. The investigation is connected to the
corresponding singular limit as Mach number goes to zero and methods for weak
solutions to the compressible Navier-Stokes system.

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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con