Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $L^2$-critical nonuniqueness for the 2D Navier-Stokes equations   In this paper, we consider the 2D incompressible Navier-Stokes equations on
the torus. It is well known that for any $L^2$ divergence-free initial data,
there exists a global smooth solution that is unique in the class of $C_t L^2$
weak solutions. We show that such uniqueness would fail in the class $C_t L^p$
if $ p<2$. The non-unique solutions we constructed are almost $L^2$-critical in
the sense that $(i)$ they are uniformly continuous in $L^p$ for every $p<2$;
$(ii)$ the kinetic energy agrees with any given smooth positive profile except
on a set of arbitrarily small measure in time.

22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph