Work

Stability of fluids in spacetimes with decelerated expansion

Year: 2026

Type: article

Abstract: We prove global existence for the relativistic Euler equations on expanding spacetimes under the weakest admissible assumptions on the spacetime expansion rate and the fluid sound speed. In contrast to all previous results on the fluid stabilization in expanding spacetimes, we consider decelerated spacetimes, which introduce new, highly singular terms into the fluid equations that cannot be analyzed using existing methods. To control these terms, we introduce a new energy method that interpolates decay between the density and velocity variables, yielding optimal decay. In a complementary paper, we present numerical evidence supporting the sharpness of this method. In particular, we conjecture that global existence fails under weaker assumptions on the expansion rate and sound speed.

Source: Annales de l Institut Henri Poincaré C Analyse Non Linéaire

DOI: 10.4171/aihpc/197

Authors: David Fajman, Maximilian Ofner, Todd Oliynyk, Zoe Wyatt

Institutions: University of Vienna, Monash University, University of Cambridge

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $700

Funder: Austrian Science Fund