Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On similarity solutions to the multidimensional aggregation equation   We study similarity solutions to the multidimensional aggregation equation
$u_t+\Div(uv)=0$, $v=-\nabla K*u$ with general power-law kernels
$K(x)=|x|^\alpha,\alpha\in (2-d,2)$. We analyze the equation in different
regimes of the parameter $\alpha$. In the case when $\alpha\in [4-d,2)$, we
give a characterization all the "first kind" radially symmetric similarity
solutions. We prove that any such solution is a linear combination of a delta
ring and a delta mass at the origin. On the other hand, when $\alpha\in
(2-d,4-d)$, we show that there exist multi delta-ring similarity solutions in
$R^d$. In particular, our results imply that multi delta-ring similarity
solutions exist in 3D if $\alpha$ is just a little bit below 1.

1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas