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

2025/01/21 by Jingya Zhao, Zhao, Jingya
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2501.12103

openalex publication_date 2025/01/21 · openalex created_date 2025/01/24 · openalex updated_date 2026/07/31

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 \citeChristodoulou86 and Klainerman \citeKlainerman86. 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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