Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Construction of type II blow-up solutions for the energy-critical wave
  equation in dimension 5   We consider the semilinear wave equation with focusing energy-critical
nonlinearity in space dimension 5 with radial data. It is known that a solution
$(u, \partial_t u)$ which blows up at $t = 0$ in a neighborhood (in the energy
norm) of the family of solitons $W_\lambda$, asymptotically decomposes in the
energy space as a sum of a bubble $W_\lambda$ and an asymptotic profile
$(u_0^*, u_1^*)$, where $\lim_{t\to 0}\lambda(t)/t = 0$ and $(u^*_0, u^*_1) \in
\dot H^1\times L^2$. We construct a blow-up solution of this type such that
$(u^*_0, u^*_1)$ is any pair of sufficiently regular functions with $u_0^*(0) >
0$. For these solutions the concentration rate is $\lambda(t) \sim t^4$. We
also provide examples of solutions with concentration rate $\lambda(t) \sim
t^{\nu + 1}$ for $\nu > 8$, related to the behaviour of the asymptotic profile
near the origin.

21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg