  In this paper, we study the ill-posdness of the Cauchy problem for semilinear
wave equation with very low regularity, where the nonlinear term depends on $u$
and $\partial_t u$. We prove a ill-posedness result for the "defocusing" case,
and give an alternative proof for the supercritical "focusing" case, which
improves our previous result in Chin. Ann. Math. Ser. B 26(3), 361-378, 2005.
