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

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.

31 pages