Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Shape Design for the Time-dependent Navier--Stokes Flow   This paper is concerned with the problem of shape optimization of
two-dimensional flows governed by the time-dependent Navier-Stokes equations.
We derive the structures of shape gradients with respect to the shape of the
variable domain for time-dependent cost functionals by using the state
derivative with respect to the shape of the fluid domain and its associated
adjoint state. Finally we apply a gradient type algorithm to our problem and
numerical examples show that our theory is useful for practical purpose and the
proposed algorithm is feasible in low Reynolds number flow.

35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an