Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Are the incompressible 3d Navier-Stokes equations locally ill-posed in
  the natural energy space?   An important open problem in the theory of the Navier-Stokes equations is the
uniqueness of the Leray-Hopf weak solutions with $L^2$ initial data.
  In this paper we give sufficient conditions for non-uniqueness in terms of
spectral properties of a natural linear operator associated to scale-invariant
solutions recently constructed in \cite{JiaSverak}. If the spectral conditions
are satisfied, non-uniqueness and ill-posedness can appear for quite benign
compactly supported data, just at the borderline of applicability of the
classical perturbation theory. The verification of the spectral conditions
seems to be approachable by relatively straightforward numerical simulations
which involve only smooth functions.

27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg