Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A cross-diffusion system obtained via (convex) relaxation in the JKO
  scheme   In this paper, we start from a very natural system of cross-diffusion
equations which, unfortunately, is not well-posed as it is the gradient flow
for the Wasserstein distance of a functional which is not lower semi-continuous
due to lack of convexity of the integral. We then compute the convexification
of the integral and prove existence of a solution in a suitable sense for the
gradient flow of the corresponding relaxed functional. This gradient flow has
also a cross-diffusion structure but the mixture between two different regimes
which are determined by the convexification makes this study non-trivial.

27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph