Self-similar imploding solutions of the relativistic Euler equations

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 $p=\frac{1}{\ell }\varrho$ 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.

arXiv comment68 pages, 2 figures