Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the blowup and lifespan of smooth solutions to a class of 2-D
  nonlinear wave equations with small initial data   We are concerned with a class of two-dimensional nonlinear wave equations
$\p_t^2u-\div(c^2(u)\na u)=0$ or $\p_t^2u-c(u)\div(c(u)\na u)=0$ with small
initial data $(u(0,x),\p_tu(0,x))=(\ve u_0(x), \ve u_1(x))$, where $c(u)$ is a
smooth function, $c(0)\not =0$, $x\in\Bbb R^2$, $u_0(x), u_1(x)\in
C_0^{\infty}(\Bbb R^2)$ depend only on $r=\sqrt{x_1^2+x_2^2}$, and $\ve>0$ is
sufficiently small. Such equations arise in a pressure-gradient model of fluid
dynamics, also in a liquid crystal model or other variational wave equations.
When $c'(0)\not= 0$ or $c'(0)=0$, $c"(0)\not= 0$, we establish blowup and
determine the lifespan of smooth solutions.

33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess