Finite time blow up for critical wave equations in high dimensions

Details Finite time blow up for critical wave equations in high dimensions Finite time blow up for critical wave equations in high dimensions

2004-04-03

arxiv.org/abs/math/0404055v1

Mathematics

Analysis of PDEs

Scientific paper

We prove that solutions to the critical wave equation below can not be global
if the initial values are positive somewhere and nonnegative. This completes
the solution to the famous blow up conjecture about critical semilinear wave
equations of the form $\Delta u - \partial^2_t u + |u|^p = 0$ in dimensions $n
\ge 4$. The lower dimensional case $n \le 3$ was settled many years earlier.

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