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math.AP2024
Linear waves on the expanding region of Schwarzschild-de Sitter spacetimes: forward asymptotics and scattering from infinity
Louie Bernhardt
We study solutions to the linear wave equation on the cosmological region of Schwarzschild-de Sitter spacetimes. We show that all sufficiently regular finite-energy solutions to th…
math.AP2024
John's blow up examples and scattering solutions for semi-linear wave equations
Louie Bernhardt, Volker Schlue, Dongxiao Yu
In light of recent work of the third author, we revisit a classic example given by Fritz John of a semi-linear wave equation which exhibits finite in time blow up for all compactly…