<p>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.</p>

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

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

  • José A. Carrillo,
  • Gui-Qiang G. Chen,
  • Difan Yuan,
  • Ewelina Zatorska

摘要

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.