*preprint*

**Inserted:** 17 jul 2018

**Year:** 2018

**Abstract:**

We show a new example of blow-up behaviour for the prescribed $Q$-curvature
equation in dimension $6$, namely given a sequence $(V_k)\subset
C^0(\mathbb{R}^6)$ suitably converging we construct a sequence $(u_k)$ of
radially symmetric solutions to the equation $$(-\Delta)^{3} u_{k=V}_{k} e^{{6} u_{k}}
\quad \text{in }\mathbb{R}^{6,$$} with $u_k$ blowing up at the origin and on a
sphere. We also prove sharp blow-up estimates.