Exotic blowup solutions for the u5 focusing wave equation in ℝ3

Abstract

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.