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Global existence of quasilinear, nonrelativistic wave equations satisfying the null condition

Jason Metcalfe·Makoto Nakamura·Christopher D. Sogge
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Abstract

We prove global existence of solutions to multiple speed, Dirichlet-wave equations with quadratic nonlinearities satisfying the null condition in the exterior of compact obstacles. This extends the result of our previous paper by allowing general higher order terms. In the currect setting, these terms are much more difficult to handle than for the free wave equation, and we do so using an analog of a pointwise estimate due to Kubota and Yokoyama.

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Jason Metcalfe, Makoto Nakamura, Christopher D. Sogge. 2004-09-20. Global existence of quasilinear, nonrelativistic wave equations satisfying the null condition. https://arxiv.org/abs/math/0409363

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