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29 March 2024
 
  » arxiv » gr-qc/0503080

 Article overview


Blowup of smooth solutions for relativistic Euler equations
Ronghua Pan ; Joel A. Smoller ;
Date 18 Mar 2005
Subject General Relativity and Quantum Cosmology; Mathematical Physics; Analysis of PDEs | gr-qc math-ph math.AP math.MP
AbstractWe 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.
Source arXiv, gr-qc/0503080
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