  Motivated by recent breakthrough on smooth imploding solutions of
compressible Euler, we construct self-similar smooth imploding solutions of
isentropic relativistic Euler equations with isothermal equation of state
$p=\frac1\ell\varrho$ for \textit{all} $\ell>1$ in physical space dimension
$d=2,3$ and for $\ell>1$ close to 1 in higher dimensions. This work is a
crucial step toward solving the long-standing problem: finite time blow-up of
the supercritical defocusing nonlinear wave equation.
