Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak solutions to the Muskat problem with surface tension via optimal
  transport   Inspired by recent works on the threshold dynamics scheme for multi-phase
mean curvature flow (by Esedo\={g}lu-Otto and Laux-Otto), we introduce a novel
framework to approximate solutions of the Muskat problem with surface tension.
Our approach is based on interpreting the Muskat problem as a gradient flow in
a product Wasserstein space. This perspective allows us to construct weak
solutions via a minimizing movements scheme. Rather than working directly with
the singular surface tension force, we instead relax the perimeter functional
with the heat content energy approximation of Esedo\={g}lu-Otto. The heat
content energy allows us to show the convergence of the associated minimizing
movement scheme in the Wasserstein space, and makes the scheme far more
tractable for numerical simulations. Under a typical energy convergence
assumption, we show that our scheme converges to weak solutions of the Muskat
problem with surface tension. We then conclude the paper with a discussion on
some numerical experiments and on equilibrium configurations.

33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg