Failure of joint continuity for porous medium flow with fractional potential pressure

We consider $u_t=\nabla\cdot(u^{m-1}\nabla(-\Delta)^{-s}u)$ on $\R^N$. For $N\ge2$, $m>2$ and $1/2<s<1$, we prove that a global bounded energy weak solution with nonzero compactly supported bounded integrable data cannot have a jointly continuous representative at all positive times. The pressure gradient is bounded, and the transport velocity vanishes with the density. A weak moving-halfspace estimate shows that joint continuity would confine the support to a fixed bounded set after any positive time. A Fourier support estimate then gives a positive lower bound for the $L^2$ dissipation, contradicting its finite time integral. Existing global weak solutions supply a counterexample in the full energy class, for example when $N=2$, $m=3$, $s=3/4$ and $u_0=\mathbf1_{B_1}$.