Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global solvability and convergence of the Euler-Poincar\'e
  regularization of the two-dimensional Euler equations   We study the Euler-Poincar\'e equations that are the regularized Euler
equations derived from the Euler-Poincar\'e framework. It is noteworthy to
remark that the Euler-Poincar\'e equations are a generalization of two
well-known regularizations, the vortex blob method and the Euler-$\alpha$
equations. We show the global existence of a unique weak solution for the
two-dimensional (2D) Euler-Poincar\'e equations with the initial vorticity in
the space of Radon measure. This is a remarkable feature of these equations
since the existence of weak solutions with the Radon measure initial vorticity
has not been established in general for the 2D Euler equations. We also show
that weak solutions of the 2D Euler-Poincar\'e equations converge to those of
the 2D Euler equations in the limit of the regularization parameter when the
initial vorticity belongs to the space of integrable and bounded functions.

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The categories of this paper are: supr-con
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex