Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonscattering solutions and blowup at infinity for the critical wave
  equation   We consider the critical focusing wave equation
$(-\partial_t^2+\Delta)u+u^5=0$ in $\R^{1+3}$ and prove the existence of energy
class solutions which are of the form [u(t,x)=t^\frac{\mu}{2}W(t^\mu
x)+\eta(t,x)] in the forward lightcone ${(t,x)\in\R\times \R^3: |x|\leq t, t\gg
1}$ where $W(x)=(1+(1/3)|x|^2)^{-(1/2)}$ is the ground state soliton, $\mu$ is
an arbitrary prescribed real number (positive or negative) with $|\mu|\ll 1$,
and the error $\eta$ satisfies [|\partial_t \eta(t,\cdot)|_{L^2(B_t)} +|\nabla
\eta(t,\cdot)|_{L^2(B_t)}\ll 1,\quad B_t:={x\in\R^3: |x|<t}] for all $t\gg 1$.
Furthermore, the kinetic energy of $u$ outside the cone is small. Consequently,
depending on the sign of $\mu$, we obtain two new types of solutions which
either concentrate as $t\to\infty$ (with a continuum of rates) or stay bounded
but do not scatter. In particular, these solutions contradict a strong version
of the soliton resolution conjecture.

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The categories of this paper are: hep-ph
3
The categories of this paper are: physics
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an