Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Applying a phase field approach for shape optimization of a stationary
  Navier-Stokes flow   We apply a phase field approach for a general shape optimization problem of a
stationary Navier-Stokes flow. To be precise we add a multiple of the
Ginzburg--Landau energy as a regularization to the objective functional and
relax the non-permeability of the medium outside the fluid region. The
resulting diffuse interface problem can be shown to be well-posed and
optimality conditions are derived. We state suitable assumptions on the problem
in order to derive a sharp interface limit for the minimizers and the
optimality conditions. Additionally, we can derive a necessary optimality
system for the sharp interface problem by geometric variations without stating
additional regularity assumptions on the minimizing set.

35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess