Global Solutions of the One-Dimensional Compressible Euler Equations with Nonlocal Interactions via the Inviscid Limit

We are concerned with the global existence of finite-energy entropy solutions of the one-dimensional compressible Euler equations with (possibly) damping, alignment forces, and the nonlocal interactions of Newtonian repulsion and quadratic confinement. Both the polytropic gas law and the general gas law are analyzed. This is achieved by constructing a sequence of solutions of the one-dimensional compressible Navier–Stokes-type equations with density-dependent viscosity on expanding intervals with the stress-free boundary condition and then taking the vanishing viscosity limit. The main difficulties in this paper arise from the appearance of the nonlocal terms. In particular, some uniform higher moment estimates of the solutions for the compressible Navier–Stokes equations on the expanding intervals with stress-free boundary condition are obtained by careful design of the approximate initial data.