Study Nonlinear Wave Equations from the Einstein Universe
We will discuss the global existence and finite time blowup of solutions to the nonlinear wave equations on Minkowski space. The idea is to conformally embed the Minkowski space-time into the Einstein Universe with the image in a compact set, which will eliminate some complicated decay and energy estimates since these propoerties can be seen easily from the covariance of the linear wave equation. This method was used successfully for existence theory. We will show how this method can also be modified to prove the blowup easily. Some Strihartz type estimates in the Einstein Universe will also be established and used to prove some nontrivial global existence