## Exotic blow up solutions for the $\Box u^5$-focussing wave equation in $\mathbb{R}^3$

For the critical focusing wave equation $\Box u = u^5$ on $\mathbb{R}^{3+1}$ in the radial case, we construct a family of blowup solutions which are obtained from the stationary solutions $W(r)$ by means of a dynamical rescaling $\lambda(t)\frac{1}{2}W(\lambda(t)r) +$ correction with $\lambda(t) \rightarrow\infty$ as $t\rightarrow 0$. The novelty here lies with the scaling law $\lambda(t)$ which eternally oscillates between various pure-power laws.

Published in:
MICHIGAN MATHEMATICAL JOURNAL, 63, 3, 451-501
Year:
2014
Publisher:
Ann Arbor, Michigan Mathematical Journal
ISSN:
0026-2285
Keywords:
Laboratories: