Uniform boundedness of conformal energy for the 3D nonlinear wave equation

Jingya Zhao

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arXiv · 2501.12103

Uniform boundedness of conformal energy for the 3D nonlinear wave equation

Jingya Zhao

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Abstract

In this paper, we study three-dimensional nonlinear wave equations under the null condition, a fundamental model in the theory of nonlinear wave-type equations, initially investigated by Christodoulou \cite{Christodoulou86} and Klainerman \cite{Klainerman86}. For a class of large initial data, we establish global existence and linear scattering of solutions by combining refined energy estimates with a bootstrap argument. Moreover, we prove that the lower-order conformal energy remains uniformly bounded for all time.

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Jingya Zhao. 2025-01-21. Uniform boundedness of conformal energy for the 3D nonlinear wave equation. https://arxiv.org/abs/2501.12103

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