Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak Singularity for Two-Dimensional Nonlinear Equations of
  Hydrodynamics and Propagation of Shock Waves   A system of two-dimensional nonlinear equations of hydrodynamics is
considered. It is shown that for the this system in the general case a solution
with weak discontinuity-type singularity behaves as a square root of S(x,y,t),
where S(x,y,t)>0 is a smooth function. The necessary conditions and series of
corresponding differential equations are obtained for the existence of a
solution.

4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin