Results on the formation of singularities for the 1-dimensional Relativistic Euler equations

Results on the formation of singularities for the 1-dimensional Relativistic Euler equations

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Nikolaos Athanasiou, Imperial College London

Zoom link: https://princeton.zoom.us/j/4745473988

 

An archetypal phenomenon in the study of hyperbolic systems of conservation laws is the development of singularities (in particular shocks) in finite time, no matter how smooth or small the initial data are. A series of works by Lax, John et al confirmed that for some important systems, when the initial data is a smooth small perturbation of a constant state, singularity formation in finite time is equivalent to the existence of compression in the initial data (this being appropriately defined in terms of spatial gradients of the Riemann invariants). Our talk will address the question of whether this dichotomy persists for large data problems, possibly containing a far-field vacuum, at least for the system of the Relativistic Euler equations in (1+1) dimensions. I shall discuss results on both the isentropic and the non-isentropic cases.

The talk will be based on joint work with Shengguo Zhu (Shanghai Jiao-Tong): https://arxiv.org/pdf/1903.03355.pdf ,as well as upcoming work with Zhu and Tianrui Bayles-Rea (Oxford).