Establishes global existence for wave-Klein-Gordon systems with nonlinear damping induced by coefficient constraints, proved via bootstrap argument with hyperboloidal foliation and vector field methods.
Wave and Dirac equations on manifolds
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abstract
We review some recent results on geometric equations on Lorentzian manifolds such as the wave and Dirac equations. This includes well-posedness and stability for various initial value problems, as well as results on the structure of these equations on black-hole spacetimes (in particular, on the Kerr solution), the index theorem for hyperbolic Dirac operators and properties of the class of Green-hyperbolic operators.
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math.AP 1years
2025 1verdicts
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A non-linear damping structure and global stability of wave-Klein-Gordon coupled system in $\mathbb{R}^{3+1}$
Establishes global existence for wave-Klein-Gordon systems with nonlinear damping induced by coefficient constraints, proved via bootstrap argument with hyperboloidal foliation and vector field methods.