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On 4D nonlinear wave equations in exterior domains
PDE Seminar| Speaker: | Jason Metcalfe, UNC Chapel Hill |
| Location: | 3106 MSB |
| Start time: | Wed, Nov 14 2007, 4:10PM |
This talk is on a recent joint work with Y. Du, C. Sogge, and Y. Zhou. Here, we discuss two results concerning 4D wave equations in exterior domains. The first is a proof of an exterior domain analog of the 4D Strauss conjecture. The second is an exterior domain analog of a result of Hormander concerning almost global existence for quasilinear wave equations with nonlinear dependence on the solution not just its derivatives. The key to the proof is a combination of certain localized energy estimates with a certain Hardy-type inequality.