Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Concerning the pathological set in the context of probabilistic
  well-posedness   We prove a complementary result to the probabilistic well-posedness for the
nonlinear wave equation. More precisely, we show that there is a dense set $S$
of the Sobolev space of super-critical regularity such that (in sharp contrast
with the probabilistic well-posedness results) the family of global smooth
solutions, generated by the convolution with some approximate identity of the
elements of $S$, does not converge in the space of super-critical Sobolev
regularity.

23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph