In this talk, I will report our recent progress on the radial Glassey conjecture with minimal regularity assumption. More precisely, for semilinear wave equations of type $/Box u =|/partial_t u|^p$ with $p_c = 1 + 2/(n -1)<ps_c=n/2+1-1/(p-1)$. It is known that $p>p_c$ is necessary for the problem to admit global solutions and $s/ge s_c$ is necessary for the problem to be local well-posed in $H^s$. In the process, we exploit and prove a weighted fractional chain rule.

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