Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Euler-Poincar\'e equation with non-zero dispersion   We consider the Euler-Poincar\'e equation on $\mathbb R^d$, $d\ge 2$. For a
large class of smooth initial data we prove that the corresponding solution
blows up in finite time. This settles an open problem raised by Chae and Liu
\cite{Chae Liu}. Our analysis exhibits some new concentration mechanism and
hidden monotonicity formula associated with the Euler-Poincar\'e flow. In
particular we show the abundance of blowups emanating from smooth initial data
with certain sign properties. No size restrictions are imposed on the data. We
also showcase a class of initial data for which the corresponding solution
exists globally in time.

13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys