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Boundedness of the conformal hyperboloidal energy for a wave-Klein-Gordon model

Philippe G. LeFlochJes\'us OliverYoshio Tsutsumi
Dec 2022
摘要
We consider the global evolution problem for a model which couples together anonlinear wave equation and a nonlinear Klein-Gordon equation, and wasindependently introduced by LeFloch and Y. Ma and by Q. Wang. By revisiting theHyperboloidal Foliation Method, we establish that a weighted energy of thesolutions remains (almost) bounded for all times. The new ingredient in theproof is a hierarchy of fractional Morawetz energy estimates (for the wavecomponent of the system) which is defined from two conformal transformations.The optimal case for these energy estimates corresponds to using the scalingvector field as a multiplier for the wave component.
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