Construction of multi-bubble solutions for the energy-critical wave equation in dimension 5

Abstract

We prove the existence of a global solution of the energy-critical focusing wave equation in dimension 5 blowing up in infinite time at any K given points zk of R5, where K≥2. The concentration rate of each bubble is asymptotic to ckt−2 as t→∞, where the ck are positive constants depending on the distances between the blow-up points zk. This result complements previous constructions of blow-up solutions and multi-solitons of the energy-critical wave equation in various dimensions N≥3.