Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A gradient flow approach to a thin film approximation of the Muskat
  problem   A fully coupled system of two second-order parabolic degenerate equations
arising as a thin film approximation to the Muskat problem is interpreted as a
gradient flow for the 2-Wasserstein distance in the space of probability
measures with finite second moment. A variational scheme is then set up and is
the starting point of the construction of weak solutions. The availability of
two Liapunov functionals turns out to be a central tool to obtain the needed
regularity to identify the Euler-Lagrange equation in the variational scheme.

12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin