Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A connection between symmetry breaking for Sobolev minimizers and
  stationary Navier-Stokes flows past a circular obstacle   Fluid flows around a symmetric obstacle generate vortices which may lead to
symmetry breaking of the streamlines. We study this phenomenon for planar
viscous flows governed by the stationary Navier-Stokes equations with constant
inhomogeneous Dirichlet boundary data in a rectangular channel containing a
circular obstacle. In such (symmetric) framework, symmetry breaking is strictly
related to the appearance of multiple solutions. Symmetry breaking properties
of some Sobolev minimizers are studied and explicit bounds on the boundary
velocity (in terms of the length and height of the channel) ensuring uniqueness
are obtained after estimating some Sobolev embedding constants and constructing
a suitable solenoidal extension of the boundary data. We show that, regardless
of the solenoidal extension employed, such bounds converge to zero at an
optimal rate as the length of the channel tends to infinity.

28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ