Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Propagation of the mono-kinetic solution in the Cucker-Smale-type
  kinetic equations   In this paper, we study the propagation of the mono-kinetic distribution in
the Cucker-Smale-type kinetic equations. More precisely, if the initial
distribution is a Dirac mass for the variables other than the spatial variable,
then we prove that this "mono-kinetic" structure propagates in time. For that,
we first obtain the stability estimate of measure-valued solutions to the
kinetic equation, by which we ensure the uniqueness of the mono-kinetic
solution in the class of measure-valued solutions with compact supports. We
then show that the mono-kinetic distribution is a special measure-valued
solution. The uniqueness of the measure-valued solution implies the desired
propagation of mono-kinetic structure.

17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat