Stable blowup for wave equations in odd space dimensions

TL;DR

This paper proves the existence of solutions that blow up in finite time for certain wave equations in odd dimensions, extending previous results to higher dimensions and covering all energy supercritical cases.

Contribution

It establishes the existence of blowup solutions in higher odd dimensions for supercritical wave equations, generalizing prior three-dimensional results.

Findings

Existence of blowup solutions in odd dimensions $d \\geq 5$

Applicable to all energy supercritical nonlinearities

Solutions approach the ODE blowup profile in a backward lightcone

Abstract

We consider semilinear wave equations with focusing power nonlinearities in odd space dimensions $d \geq 5$. We prove that for every $p > \frac{d+3}{d-1}$ there exists an open set of radial initial data in $H^{\frac{d+1}{2}} \times H^{\frac{d-1}{2}}$ 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.