Blowup of smooth solutions for relativistic Euler equations

Details Blowup of smooth solutions for relativistic Euler equations Blowup of smooth solutions for relativistic Euler equations

2005-03-18

arxiv.org/abs/gr-qc/0503080v1

Commun.Math.Phys. 262 (2006) 729-755

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

30 pages

Scientific paper

10.1007/s00220-005-1464-9

We study the singularity formation of smooth solutions of the relativistic Euler equations in $(3+1)$-dimensional spacetime for both finite initial energy and infinite initial energy. For the finite initial energy case, we prove that any smooth solution, with compactly supported non-trivial initial data, blows up in finite time. For the case of infinite initial energy, we first prove the existence, uniqueness and stability of a smooth solution if the initial data is in the subluminal region away from the vacuum. By further assuming the initial data is a smooth compactly supported perturbation around a non-vacuum constant background, we prove the property of finite propagation speed of such a perturbation. The smooth solution is shown to blow up in finite time provided that the radial component of the initial "generalized" momentum is sufficiently large.

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