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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

Publisher:

Ann Arbor, Michigan Mathematical Journal

ISSN:

0026-2285

Keywords:

Laboratories:

Record created 2013-01-09, last modified 2018-03-13