u = q (t) r, q (t) = \frac{u _{0} ( t )}{R ( t )},

with the spatially uniform velocity divergence

\nabla \cdot u = 3 q > 0.

(2)

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.