Compressible Navier–Stokes-Yukawa equations under stability condition \(P'(\bar{\rho })+\gamma \bar{\rho }>0\) is considered, where P is the pressure, \(\bar{\rho }\) is the background density and the constant \(\gamma \in \mathbb {R}\) . We verify that the time-asymptotic shape of the solution contains a stationary diffusion wave superposing a moving diffusion wave with the propagation speed \(\sqrt{P'(\bar{\rho })+\gamma \bar{\rho }}\) , which means that the sign of \(\gamma \) determines whether the potential fluid force enhances or deduces the propagation speed of the moving diffusion wave. This is completely different from the compressible Navier–Stokes-Poisson equations in Wang and Wu (2010JDE), where the Poisson potential critically impedes the speed of propagation wave such that pointwise description of the solution only contains a stationary diffusion wave. Besides, when \(\gamma =0\) , our pointwise result is consistent with the compressible Navier–Stokes equations in Liu and Wang (1998CMP).
