2024/03/13 by José A. Carrillo, Carrillo, Jose A., Gui‐Qiang Chen +5
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2403.08576
openalex publication_date 2024/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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 nonlocal interactions: 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 under 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 for the compressible Navier-Stokes equations on expanding intervals with stress-free boundary conditions are obtained by careful design of the approximate initial data.