= Solution
The given velocity is a <homologous spherical flow>,
$$
\mathbf u=q(t)\mathbf r,
\qquad q(t)=\frac{u_0(t)}{R(t)},
$$
with the spatially uniform <velocity divergence>
$$
\nabla\mathbin\cdot\mathbf u=3q>0.
$$
Every shocked <fluid element> therefore expands rather than undergoing continued compression, and the velocity fills the remnant smoothly instead of concentrating its mass in a thin cooling shell. In the absence of radiative losses, the <entropy advection equation> then makes each element follow an <adiabatic process> after its one entropy-producing passage through the shock. This broad expanding structure is the expected <adiabatic phase of a supernova remnant>.
Back to article page
