Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universality of Euler flows and flexibility of Reeb embeddings   The dynamics of an inviscid and incompressible fluid flow on a Riemannian
manifold is governed by the Euler equations. Recently, Tao [35,36] launched a
programme to address the global existence problem for the Euler and Navier
Stokes equations based on the concept of universality. In this article we prove
that the Euler equations exhibit universality features. More precisely, we show
that any non-autonomous flow on a compact manifold can be extended to a smooth
solution of the Euler equations on some Riemannian manifold of possibly higher
dimension. The solutions we construct are stationary of Beltrami type, so they
exist for all time. Using this result, we establish the Turing completeness of
the Euler flows, i.e. that there exist solutions that encode a universal Turing
machine and, in particular, these solutions have undecidable trajectories. Our
proofs deepen the correspondence between contact topology and hydrodynamics,
which is key to establish the universality of the Reeb flows and their Beltrami
counterparts. An essential ingredient in the proofs is a novel flexibility
theorem for embeddings in Reeb dynamics in terms of an $h$-principle in contact
geometry, which unveils the flexible behavior of the steady Euler flows.

10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph