Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On existence and uniqueness of solutions to a Boussinesq system with
  nonlinear and mixed boundary conditions   We study a Boussinesq system in a bounded domain with an outlet boundary
portion where fluid can leave or re-enter. On this boundary part, we consider a
do-nothing condition for the fluid flow, and a new artificial condition for the
heat transfer that couples nonlinearly the fluid velocity and temperature. The
latter can be further adjusted if convective or conductive phenomena are
dominant. We prove existence and, in some cases, uniqueness of weak solutions
to stationary and evolutionary problems by a fixed point strategy under
suitable assumptions on the data. A variety of numerical tests shows the
improved performance of the new artificial condition with respect to other
standard choices in the literature.

23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph