Global Existence for a Coupled Wave System related to the Strauss Conjecture
Undergraduate: David Spencer
Faculty Advisor: Jason Metcalfe
Department: Mathematics
Wave equations model a wide variety of phenomena in diverse fields such as optics, geology, and cosmology. Therefore, it is of interest to determine which wave equations have solutions defined for all time given small initial data, and which exhibit blow-up of solutions in finite time for arbitrarily small initial data. In this project, a coupled system of semilinear wave equations is considered, and a small data global existence result related to the Strauss conjecture is proved. Previous results have shown that one of the powers may be reduced below the critical power for the Strauss conjecture provided the other power sufficiently exceeds such. The stability of such results under asymptotically flat perturbations of the space-time where an integrated local energy decay estimate is available is established.