In this talk, we answer the open question on stability of a Riemann shock (as an entropy solution to Euler) in a class of inviscid limits from the physical system. For the physical system, we consider the so-called Brenner-Navier-Stokes-Fourier system. This system was proposed by Howard Brenner as a continuum model for compressible fluid flow, based on 'bi-velocity theory' which indicates the existence of two different velocities: one is the mass velocity that appears in the classical compressible fluid model, and the other is the volume velocity is something new to define momentum, work, energy and viscous stress. The two velocities are different if the density is not uniform as in compressible flow.