Global existence of null-form wave equations in exterior domains
The major innovations of this paper regard the variable-coefficient Keel-Smith-Sogge (KSS) estimate. Firstly, the authors prove the KSS estimate for the perturbed wave equaton in the multiple speed setting. Having such estimates for the perturbed equation allows the authors to apply the KSS estimates even for terms of the highest order. This was not previously possible for quasilinear equations as there was a loss of regularity resulting from the occurrence of second derivatives. As such, the authors may prove global existence using only energy methods. In particular, the decay estimates that the authors shall employ do not require direct estimation of the fundamental solution of the linear wave equation. Thus the authors provide a proof of global existence of solutions to quasilinear wave equations satisfying the null condition in certain exterior domains.
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