Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mean Field Limit for Coulomb-Type Flows   We establish the mean-field convergence for systems of points evolving along
the gradient flow of their interaction energy when the interaction is the
Coulomb potential or a super-coulombic Riesz potential, for the first time in
arbitrary dimension. The proof is based on a modulated energy method using a
Coulomb or Riesz distance, assumes that the solutions of the limiting equation
are regular enough and exploits a weak-strong stability property for them. The
method can handle the addition of a regular interaction kernel, and applies
also to conservative and mixed flows. In the appendix, it is also adapted to
prove the mean-field convergence of the solutions to Newton's law with Coulomb
or Riesz interaction in the monokinetic case to solutions of an Euler-Poisson
type system.

11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat