Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scattering for the radial 3d cubic wave equation   Consider the Cauchy problem for the radial cubic wave equation in 1+3
dimensions with either the focusing or defocusing sign. This problem is
critical in $\dot{H}^{\frac{1}{2}} \times \dot{H}^{-\frac{1}{2}}$ and
subcritical with respect to the conserved energy. Here we prove that if the
critical norm of a solution remains bounded on the maximal time-interval of
existence, then the solution must in fact be global-in-time and scatter to free
waves as $t \to \pm \infty$.

1
The categories of this paper are: cs
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an