Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Incompressible Averaged Lagrangian Hydrodynamics   This paper is devoted to the geometric analysis of the incompressible
averaged Euler equations on compact Riemannian manifolds with boundary. The
equation also coincides with the model for a second-grade non-Newtonian fluid.
We study the analytical and geometrical properties of the Lagrangian flow map.
We prove existence and uniqueness of smooth-in-time solutions for initial data
in $H^s$, $s > n/2 +1$ by establishing the existence of smooth geodesics of a
new weak right invariant metric on new subgroups of the volume-preserving
diffeomorphism group. We establish smooth limits of zero viscosity for the
second-grade fluids equations even on manifolds with boundary. We prove that
the weak curvature operator of the weak invariant metric is continuous in the
$H^s$ topology for $s> n/2+2$, thus proving existence and uniqueness for the
Jacobi equation. We show that this new metric stabilizes the Lagrangian flow of
the original Euler equations by changing the sign of the sectional curvature.

14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an