Rayleigh collapse of a spherical cavity
= Rayleigh collapse of a spherical cavity
{c}
A vacuum cavity of radius $a(t)$ in an infinite inviscid incompressible fluid of density $\rho$ and far-field pressure $p_0$ obeys
$$
a\ddot a+\frac32\dot a^2=-\frac{p_0}{\rho}.
$$
If $a(0)=a_0$ and $\dot a(0)=0$, its collapsing branch satisfies
$$
\dot a=-\sqrt{\frac{2p_0}{3\rho}
\left(\frac{a_0^3}{a^3}-1\right)}.
$$