Self-similar imploding solutions of the relativistic Euler equations

Feng Shao; Dongyi Wei; Zhifei Zhang

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arXiv · 2403.11471

Self-similar imploding solutions of the relativistic Euler equations

Feng Shao·Dongyi Wei·Zhifei Zhang

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Abstract

Motivated by recent breakthrough on smooth imploding solutions of compressible Euler, we construct self-similar smooth imploding solutions of isentropic relativistic Euler equations with isothermal equation of state $p=\frac1\ell\varrho$ for \textit{all} $\ell>1$ in physical space dimension $d=2,3$ and for $\ell>1$ close to 1 in higher dimensions. This work is a crucial step toward solving the long-standing problem: finite time blow-up of the supercritical defocusing nonlinear wave equation.

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Feng Shao, Dongyi Wei, Zhifei Zhang. 2024-03-18. Self-similar imploding solutions of the relativistic Euler equations. https://arxiv.org/abs/2403.11471

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