For gamma = 5/3, corresponding to a monatomic gas, there exist smooth initial data for which the 3-D compressible Navier-Stokes equations blow up in finite time in a self-similar implosion.
On blow-up for the supercritical defocusing nonlinear wave equation
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In this paper, we consider the defocusing nonlinear wave equation $-\partial_t^2u+\Delta u=|u|^{p-1}u$ in $\mathbb R\times \mathbb R^d$. Building on our companion work ({\it \small Self-similar imploding solutions of the relativistic Euler equations}), we prove that for $d=4, p\geq 29$ and $d\geq 5, p\geq 17$, there exists a smooth complex-valued solution that blows up in finite time.
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Blow-up of the 3-D compressible Navier-Stokes equations for monatomic gases
For gamma = 5/3, corresponding to a monatomic gas, there exist smooth initial data for which the 3-D compressible Navier-Stokes equations blow up in finite time in a self-similar implosion.