Bounds on the speed of type II blowup for the energy critical wave equation in the radial case
Abstract
We consider the focusing energycritical wave equation in space dimension $N\in \{3, 4, 5\}$ for radial data. We study type II blowup 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 blowup 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2015
 arXiv:
 arXiv:1509.03331
 Bibcode:
 2015arXiv150903331J
 Keywords:

 Mathematics  Analysis of PDEs
 EPrint:
 22 pages