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 Christodoulou86 and Klainerman 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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