99 citations · 687 across the 54 of their papers we have counts for
37 papers · 1 filter
Future Stability of Tilted Two-Fluid Bianchi I Spacetimes
Grigorios Fournodavlos, Elliot Marshall, Todd A. Oliynyk
We establish the nonlinear stability to the future of tilted two-fluid Bianchi I solutions to the Einstein-Euler equations with positive cosmological constant and linear equations…
Past instability of FLRW solutions of the Einstein-Euler-scalar field equations for linear equations of state with
Florian Beyer, Elliot Marshall, Todd A. Oliynyk
Using numerical methods, we examine, under a Gowdy symmetry assumption, the dynamics of nonlinearly perturbed FLRW fluid solutions of the Einstein-Euler-scalar field equations in t…
On the fractional density gradient blow-up conjecture of Rendall
Todd A. Oliynyk
On exponentially expanding Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes, there is a distinguished family of spatially homogeneous and isotropic solutions to the relativist…
Past stability of FLRW solutions to the Einstein-Euler-scalar field equations and their big bang singularites
Florian Beyer, Todd A. Oliynyk
We establish, in spacetime dimensions , the nonlinear stability in the contracting direction of Friedmann-Lemaître-Robertson-Walker (FLRW) solutions to the Einstein-Euler-…
Future instability of FLRW fluid solutions for linear equations of state with
Florian Beyer, Elliot Marshall, Todd A. Oliynyk
Using numerical methods, we examine the dynamics of nonlinear perturbations in the expanding time direction, under a Gowdy symmetry assumption, of FLRW fluid solutions to the Einst…
On the stability of relativistic perfect fluids with linear equations of state where
Elliot Marshall, Todd A. Oliynyk
For , we consider the stability of two distinct families of spatially homogeneous solutions to the relativistic Euler equations with a linear equation of state on e…
Future global existence and stability of de Sitter-like solutions to the Einstein-Yang-Mills equations in spacetime dimensions
Chao Liu, Todd A. Oliynyk, Jinhua Wang
We establish the global existence and stability to the future of non-linear perturbation of de Sitter-like solutions to the Einstein-Yang-Mills system in spacetime dimen…
Localized big bang stability for the Einstein-scalar field equations
Florian Beyer, Todd A. Oliynyk
We prove the nonlinear stability in the contracting direction of Friedmann-Lemaître-Robertson-Walker (FLRW) solutions to the Einstein-scalar field equations in spacetime…
Stability of Asymptotic Behavior Within Polarised -Symmetric Vacuum Solutions with Cosmological Constant
Ellery Ames, Florian Beyer, James Isenberg +1
We prove the nonlinear stability of the asymptotic behavior of perturbations of subfamilies of Kasner solutions in the contracting time direction within the class of polarised $T^2…
Stability of AVTD Behavior within the Polarized -symmetric vacuum spacetimes
Ellery Ames, Florian Beyer, James Isenberg +1
We prove stability of the family of Kasner solutions within the class of polarized -symmetric solutions of the vacuum Einstein equations in the contracting time direction with…
Stabilizing relativistic fluids on spacetimes with non-accelerated expansion
David Fajman, Todd A. Oliynyk, Zoe Wyatt
We establish global regularity and stability for the irrotational relativistic Euler equations with equation of state , where , for small initial…
Future global stability for relativistic perfect fluids with linear equations of state where
Todd A. Oliynyk
We establish the future stability of nonlinear perturbations of a class of homogeneous solutions to the relativistic Euler equations with a linear equation of state on expon…
Cosmological Newtonian limits on large spacetime scales
Chao Liu, Todd A. Oliynyk
We establish the existence of -parameter families of -dependent solutions to the Einstein-Euler equations with a positive cosmological constant and a linear equation of…
Dynamical relativistic liquid bodies I: constraint propagation
Todd A. Oliynyk
We introduce a new wave formulation for the relativistic Euler equations with vacuum boundary conditions that consists of a system of non-linear wave equations in divergence form w…
Newtonian Limits of Isolated Cosmological Systems on Long Time Scales
Chao Liu, Todd A. Oliynyk
We establish the existence of -parameter families of -dependent solutions to the Einstein-Euler equations with a positive cosmological constant and a linear equation of…
Future stability of the FLRW fluid solutions in the presence of a positive cosmological constant
Todd A. Oliynyk
We introduce a new method for establishing the future non-linear stability of perturbations of FLRW solutions to the Einstein-Euler equations with a positive cosmological constant…
Dynamical compact elastic bodies in general relativity
Lars Andersson, Todd A. Oliynyk, Bernd G. Schmidt
We prove the local existence of solutions to the Einstein-Elastic equations that represent self-gravitating, relativistic elastic bodies with compact support.
The Newtonian limit on cosmological scales
Todd A. Oliynyk
We establish the existence of a wide class of inhomogeneous relativistic solutions to the Einstein-Euler equations that are well approximated on cosmological scales by solutions of…
Lagrange coordinates for the Einstein-Euler equations
Todd A. Oliynyk
We derive a new symmetric hyperbolic formulation of the Einstein-Euler equations in Lagrange coordinates that are adapted to the Frauendiener-Walton formulation of the Euler equati…
Cosmological Newtonian limit
Todd A. Oliynyk
We describe a wide class of inhomogeneous relativistic solutions that are well approximated on cosmological scales by solutions of Newtonian gravity. Error estimates measuring the…
Dynamical elastic bodies in Newtonian gravity
Lars Andersson, Todd A. Oliynyk, Bernd G. Schmidt
Well-posedness for the initial value problem for a self-gravitating elastic body with free boundary in Newtonian gravity is proved. In the material frame, the Euler-Lagrange equati…
There are no magnetically charged particle-like solutions of the Einstein Yang-Mills equations for Abelian models
Mark Fisher, Todd A. Oliynyk
We prove that there are no magnetically charged particle-like solutions for Abelian models in Einstein Yang-Mills, but for non-Abelian models the possibility remains open. An analy…
On the existence of solutions to the relativistic Euler equations in 2 spacetime dimensions with a vacuum boundary
Todd A. Oliynyk
We prove the existence of a wide class of solutions to the isentropic relativistic Euler equations in 2 spacetime dimensions with an equation of state of the form that hav…
Cosmological post-Newtonian expansions to arbitrary order
Todd A. Oliynyk
We prove the existence of a large class of one parameter families of solutions to the Einstein-Euler equations that depend on the singular parameter $\ep=v_T/c$ $(0<\ep < \ep_0)$,…