4 papers
Nonlinear stability of Einstein-de Sitter universes
Louie Bernhardt, David Fajman, Zoe Wyatt
The Einstein-de Sitter universe is the prevailing model used in cosmology to describe the cold dark matter-dominated epoch of the universe. This model is a spatially homogeneous an…
Future stability of solutions of the Einstein-nonlinear scalar field system with decelerated expansion
Louie Bernhardt
We study solutions to the Einstein equations coupled to a nonlinear scalar field with exponential potential. This system admits Friedmann-Lemaître-Robertson-Walker solutions underg…
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…
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…