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We consider the focusing energy-critical wave equation in space dimension   $N \in \{3, 4, 5\}$   for radial data. We study type II blow-up solutions which concentrate one bubble of energy. It is known that such solutions decompose in the energy space as a sum of the bubble and an asymptotic profile. We prove bounds on the blow-up speed in the case when the asymptotic profile is sufficiently regular. These bounds are optimal in dimension   $N = 5$  . We also prove that if the asymptotic profile is sufficiently regular, then it cannot be strictly negative at the origin.

Bounds on the Speed of Type II Blow-up for the Energy Critical Wave Equation in the Radial Case