Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variational resolution of outflow boundary conditions for incompressible
  Navier-Stokes   This paper focuses on the so-called Weighted Inertia-Dissipation-Energy
(WIDE) variational approach for the approximation of unsteady Leray-Hopf
solutions of the incompressible Navier-Stokes system. Initiated in [56], this
variational method is here extended to the case of non-Newtonian fluids with
power-law index $r\geq11/5$ in three space dimensions and large nonhomogeneous
data. Moreover, boundary conditions are not imposed on some parts of
boundaries, representing, e.g., outflows. Correspondingly, natural boundary
conditions arise from the minimization. In particular, at walls we recover
boundary conditions of Navier-slip type. At outflows and inflows, we obtain the
condition
$-\frac12|\boldsymbol{v}|^2\boldsymbol{n}+\mathbb{T}\boldsymbol{n}=0$. This
provides the first theoretical explanation for the onset of such boundary
conditions.

32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th