Stabilizing relativistic fluids on spacetimes with non-accelerated expansion

Abstract

We establish global regularity and stability for the irrotational relativistic Euler equations with equation of state $\overline{p}=K\overline{\rho }$, where $0<K<1/3$, for small initial data in the expanding direction of FLRW spacetimes of the form $(\mathbb R\times\mathbb T^3,-d\tb^2+\tb^2δ_{ij} dx^i dx^j)$. This provides the first case of non-dust fluid stabilization by spacetime expansion where the expansion rate is of power law type but non-accelerated. In particular, the time integral of the inverse scale factor diverges as $t\to \infty$.

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Cited by in corpus (16)

• Future global stability for relativistic perfect fluids with linear equations of state $p=K\rho$ where $1/3<K<1/2$
• Self-Similar Solutions to the Compressible Euler Equations and their Instabilities
• Recent developments in mathematical aspects of relativistic fluids
• The Stability of Relativistic Fluids in Linearly Expanding Cosmologies
• On the stability of relativistic perfect fluids with linear equations of state $p=K\rho$ where $1/3<K<1$
• Stable cosmologies with collisionless charged matter
• Future dynamics of FLRW for the massless-scalar field system with positive cosmological constant
• Future instability of FLRW fluid solutions for linear equations of state $p=K\rho$ with $1/3<K<1$
• Localized big bang stability for the Einstein-scalar field equations
• Slowly expanding stable dust spacetimes
• Stability of AVTD Behavior within the Polarized $T^2$-symmetric vacuum spacetimes
• Explorations of the infinite regions of space-time
• Decay and Subluminality of Modes of all Wave Numbers in the Relativistic Dynamics of Viscous and Heat Conductive Fluids
• Stability of Asymptotic Behavior Within Polarised $T^2$-Symmetric Vacuum Solutions with Cosmological Constant
• Blowups for a class of second order nonlinear hyperbolic equations: A reduced model of nonlinear Jeans instability
• Dynamics of a nonminimally coupled scalar field in asymptotically $Ad{S}_4$ spacetime