Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ill-posedness of the Thirring model below the critical regularity   We consider a nonlinear $L^2$-critical nonlinear Dirac equation in one space
dimension known as the Thirring model. Global well-posedness in $L^2$ for this
equation was proved by Candy. Here we prove that the equation is ill posed in
$L^p$ for $1 \le p < 2$, and in the massless case also in $H^s$ with $s < 0$.

29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio