  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.
