Radiation of the Energy-Critical Wave Equation with Compact Support
Journal of Functional Analysis(2024)
摘要
We prove exterior energy lower bounds for (nonradial) solutions to the energy-critical nonlinear wave equation in space dimensions 3≤d≤5, with compactly supported initial data. In particular, it is shown that nontrivial global solutions with compact spatial support must be radiative in a sharp sense. In space dimensions 3 and 4, a nontrivial soliton background is also considered. As an application, we obtain partial results on the rigidity conjecture concerning solutions with the compactness property, including a new proof for the global existence of such solutions.
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关键词
Energy channel,Rigidity conjecture,Unique continuation,Conformal inversion
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