Global regularity and sharp decay rates for the one-dimensional hypo-viscous compressible Navier-Stokes equations in critical Besov spaces

In this paper, we study the global regularity of the one-dimensional hypo-viscous compressible Navier--Stokes equations in the critical Besov spaces, where the initial data are close to the constant equilibrium state. We introduce an effective velocity, constructed as a combination of the density an