Stable blowup for wave equations in odd space dimensions

Abstract

We consider semilinear wave equations with focusing power nonlinearities in odd space dimensions d≥5. We prove that for every p>d+3d−1 there exists an open set of radial initial data in Hd+12×Hd−12 such that the corresponding solution exists in a backward lightcone and approaches the ODE blowup profile. The result covers the entire range of energy supercritical nonlinearities and extends our previous work for the three-dimensional radial wave equation to higher space dimensions.