Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Time-dependent focusing Mean-Field Games: the sub-critical case   We consider time-dependent viscous Mean-Field Games systems in the case of
local, decreasing and unbounded coupling. These systems arise in mean-field
game theory, and describe Nash equilibria of games with a large number of
agents aiming at aggregation. We prove the existence of weak solutions that are
minimisers of an associated non-convex functional, by rephrasing the problem in
a convex framework. Under additional assumptions involving the growth at
infinity of the coupling, the Hamiltonian, and the space dimension, we show
that such minimisers are indeed classical solutions by a blow-up argument and
additional Sobolev regularity for the Fokker-Planck equation. We exhibit an
example of non-uniqueness of solutions. Finally, by means of a contraction
principle, we observe that classical solutions exist just by local regularity
of the coupling if the time horizon is short.

31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc