1201.3258 (Roland Donninger et al.)

Nonscattering solutions and blowup at infinity for the critical wave
equation    [PDF]

Roland Donninger, Joachim Krieger

We consider the critical focusing wave equation $(-\partial_t^2+\Delta)u+u^5=0$ in $\R^{1+3}$ and prove the existence of energy class solutions which are of the form [u(t,x)=t^\frac{\mu}{2}W(t^\mu x)+\eta(t,x)] in the forward lightcone ${(t,x)\in\R\times \R^3: |x|\leq t, t\gg 1}$ where $W(x)=(1+(1/3)|x|^2)^{-(1/2)}$ is the ground state soliton, $\mu$ is an arbitrary prescribed real number (positive or negative) with $|\mu|\ll 1$, and the error $\eta$ satisfies [|\partial_t \eta(t,\cdot)|_{L^2(B_t)} +|\nabla \eta(t,\cdot)|_{L^2(B_t)}\ll 1,\quad B_t:={x\in\R^3: |x|View original: http://arxiv.org/abs/1201.3258