Stable self-similar blow up for energy subcritical wave equations
We consider the semilinear wave equation partial derivative(2)(t)psi - Delta psi = vertical bar psi vertical bar(p-1)psi for 1 < p <= 3 with radial data in R-3. This equation admits an explicit spatially homogeneous blow up solution psi(T) given by psi(T)(t, x) = kappa(p)(T - t)(-2/p-1) where T > 0 and kappa(p) is a p-dependent constant. We prove that the blow up described by psi(T) is stable against small perturbations in the energy topology. This complements previous results by Merle and Zaag. The method of proof is quite robust and can be applied to other self-similar blow up problems as well, even in the energy supercritical case.