FINITE TIME BLOW UP FOR CRITICAL WAVE EQUATIONS IN HIGH DIMENSIONS : COMPLETION OF THE PROOF OF STRAUSS CONJECTURE

@inproceedings{Zhang2004FINITETB,
title={FINITE TIME BLOW UP FOR CRITICAL WAVE EQUATIONS IN HIGH DIMENSIONS : COMPLETION OF THE PROOF OF STRAUSS CONJECTURE},
author={Qi S. Zhang},
year={2004}
}

We prove that solutions to the critical wave equation (1.1) with dimension n ≥ 4 can not be global if the initial values are positive somewhere and nonnegative. This completes the solution to the famous conjecture about semilinear wave equations of the form ∆u− ∂ t u + |u| = 0. The rest of the cases, the lower dimensional case n ≤ 3, and the sub or super critical cases were settled many years earlier by the work of several authors.