Momentum-conserving supernova-remnant expansion ($R\propto t^{1/4}$)

In the ideal cooled-shell limit with negligible continuing interior pressure, swept-up mass in a uniform medium scales as $R^3$. Constant radial shell momentum then gives $R^3\dot{R}=\mathrm{const}$ and $R\propto t^{1/4}$. This differs from an energy-conserving blast wave or a pressure-driven snowplough.