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arXiv · 2212.01184

Global stability for nonlinear wave equations satisfying a generalized null condition

John Anderson·Samuel Zbarsky
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Abstract

We prove global stability for a system of nonlinear wave equations satisfying a generalized null condition. The generalized null condition allows for null forms whose coefficients have bounded $C^k$ norms. We prove both pointwise decay and improved decay of good derivatives using bilinear energy estimates and duality arguments. Combining this strategy with the $r^p$ estimates of Dafermos--Rodnianski then allows us to prove global stability. The proof requires analyzing the geometry of intersecting null hypersurfaces adapted to solutions of wave equations.

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John Anderson, Samuel Zbarsky. 2022-12-02. Global stability for nonlinear wave equations satisfying a generalized null condition. https://arxiv.org/abs/2212.01184

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