  In this paper, a class of non-Newton filtration equations with singular
potential and logarithmic nonlinearity under initial-boundary condition is
investigated. Based on potential well method and Hardy-Sobolev inequality, the
global existence of solutions is derived when the initial energy $J(u_0)$ is
subcritical($J(u_0)<d$), critical($J(u_0)=d$) with $d$ being the mountain-pass
level. Finite time blow-up results are obtained as well when the initial energy
$J(u_0)$ satisfies specific conditions. Moreover, the upper and lower bounds of
the blow-up time are given.
