$L^{2}-L^{\infty}$ decay estimates and inviscid limits for Global smooth solutions to the compressible Navier-Stokes-Riesz system

We study the Cauchy problem in $\mathbb{R}^{3}$ for the repulsive compressible Navier-Stokes-Riesz system with Riesz exponent $0<s<1$ and viscosity $0<\varepsilon\leq1$, where the Riesz interaction $\nabla(-Δ)^{-s}(ρ-\barρ)$ is a generalization of the Coulomb interaction for electrons. For small per