Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the existence and uniqueness of solutions to time-dependent
  fractional MFG   We establish existence and uniqueness of solutions to evolutive fractional
Mean Field Game systems with regularizing coupling, for any order of the
fractional Laplacian $s\in(0,1)$. The existence is addressed via the vanishing
viscosity method. In particular, we prove that in the subcritical regime
$s>1/2$ the solution of the system is classical, while if $s\leq 1/2$ we find a
distributional energy solution. To this aim, we develop an appropriate
functional setting based on parabolic Bessel potential spaces. We show
uniqueness of solutions both under monotonicity conditions and for short time
horizons.

21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio